To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW The derivative of `tan^(1) 2x/(1x^2)` with respect to `sin^(1) 2x/(1x^2)`, isAbout Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How works Test new features Press Copyright Contact us CreatorsPochodna 2*sec(x)^2*tan(x) po x = 4*sec(x)^2*tan(x)^22*sec(x)^4 Pokaż rozwiązanie "krok po kroku" Rysuj Edytuj Bezpośredni link Wartość na x= Kalkulator pochodnych oblicza pochodną funkcji w odniesieniu do danej zmiennej za pomocą analizy zróżnicowania Obsługiwane są pochodne do 10 stopnia
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2 sec^2x tan x derivative-Find the Derivative d/dx y=2sec(x)tan(x) Since is constant with respect to , the derivative of with respect to is Differentiate using the Product Rule which states that is where and The derivative of with respect to is Multiply by by adding the exponents$\endgroup$ – Simon S Nov 1 '14 at 2253 2 $\begingroup$ It's important to look into the problem thoroughly before coming here
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For more cool math videos visit my site at mathgotservedcom or http//youtubecom/mathsgotservedWhat Is The Greatest Common Factor Of 4k, 18k4, And 12? · We know that, (1) d dx (secx) = secxtanx (2) d dx (tanx) = sec2x Here, y = sec2x tan2x Diffwrt x , using Chain Rule dy dx = 2secx d dx (secx) 2tanx d dx (tanx) ∴ dy dx = 2secx ⋅ secxtanx 2tanx ⋅ sec2x ∴ dy dx = 2sec2xtanx 2sec2xtanx
2909 · Using the product rule, the derivative of tan^2x is 2tan(x)sec 2 (x) Finding the derivative of tan^2x using the chain rule The chain rule is useful for finding the derivative of a function which could have been differentiated had it been in x, but it is in the form of another expression which could also be differentiated if it stood on its own · Secant is the reciprocal of the cosine The secant of an angle designated by a variable x is notated as sec(x) The derivative rule for sec(x) is given as d ⁄ dx sec(x) = tan(x)sec(x) This derivative rule gives us the ability to quickly and directly differentiate sec(x)Liczba wierszy 7 · 0210 · Using the product rule, the derivative of sec^2x is 2sec^2(x)tan(x) Finding the
· If the derivative of a is b, then the integral of b is a C, where C is a constant This tells us that to check our work, we can take the integral of 2sec 2 x tan x, and we should get sec 2 xThe differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change with respect to a variableFor example, the derivative of the sine function is written sin′(a) = cos(a), meaning that the rate of change of sin(x) at a particular angle x = a is given by the cosine of that angle0909 · Using the product rule, the derivative of sin^2x is 2sin(x)cos(x) Finding the derivative of sin^2x using the chain rule The chain rule is useful for finding the derivative of a function which could have been differentiated had it been in x, but it is in the form of another expression which could also be differentiated if it stood on its own
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· How to Take the Derivative of Tan x You can take the derivative of tan x using the quotient rule That's because of a basic trig identity, which is a quotient of the sine function and cosine function tan(x) = sin(x) / cos(x) Step 1 Name the numerator (top term) in the quotient g(x) and the denominator (bottom term) h(x)1311 · From above, we found that the first derivative of sec(2x) = 2sec(2x)tan(2x) So to find theSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more
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By signing up, you'll get thousands of stepbystep solutions to your homework questions You canProve that the derivative of tan (x) is sec^2 (x) Let y = tan (x) Recall the definition of tan (x) as sin (x)/cos (x) Therefore y = sin (x)/cos (x) Use the quotient rule, which states that for y = f (x)/g (x), dy/dx = (f' (x)g (x) f (x)g' (x))/g 2 (x) with f (x) = sin (x) and g (x) = cos (x) · (tan x)' = sec^2 x Let f(x) = tanx We know that tanx = sinx/ cosx ==> f(x) = sinx/ cosx Now to differenctiate f(x) we will use the chain rule f(x) = u/v such that u= sinx ==> u' = cosx
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Find the 2nd Derivative y=tan(x) The derivative of with respect to is Find the second derivative Tap for more steps Differentiate using the chain rule, which states that is where and Tap for more steps To apply the Chain Rule, set as Differentiate using the · Example 17 Compute the derivative tan x Let f (x) = tan x We need to find f' (x) We know that f' (x) = lim┬ (ℎ→0) f〖 (𝑥 ℎ) − f (x)〗/ℎ Here, f (x) = tan x f (x ℎ) = tan (x ℎ) Putting values f' (x) = lim┬ (ℎ→0) tan〖 (𝑥 ℎ) −tan𝑥 〗/ℎ = lim┬ (ℎ→0) 1/ℎ ( tan (x h) – tan x) = lim┬ (ℎ→0) 1/ℎ (sin (𝑥 ℎ)/cos (𝑥 ℎ) − · Therefore, it is natural for $\sec^2(x)$ to be the derivative of $\tan(x)$ The same technique will work for $\sin(x), \cos(x)$, and many others If you are uncomfortable with the algebra then it is best draw a function and its derivative on graph paper
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Vahin8411 Vahin8411 Math Secondary School How do find the derivative of y=(sec)2x(tan)2x?For those with a technical background, the following section explains how the Derivative Calculator works First, a parser analyzes the mathematical function It transforms it into a form that is better understandable by a computer, namely a tree (see figure below) In doing this, the Derivative Calculator has to respect the order of operations A specialty in mathematical expressions is that the multiplication sign can be left out sometimes, for example we write "5x" instead of "5*x"Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history
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· The derivative of sec2 (x) is 2sec2 (x) tan (x) The chain rule states that the derivative of f(g(x)) is equal to f ' (g(x)) ⋅ g ' (x)0211 · We can use the chain rule to find the derivative of 2sec 2 (2x) (bearing in mind that the derivative of sec^2(x) is 2sec 2 (x)tan(x)) and it gives us a result of 8sec 2 (2x)tan(2x) The second derivative of tan(2x) is 8sec 2 (2x)tan(2x)Derivative Calculator Derivative of 2*sec (x)^2*tan (x) by x = 4*sec (x)^2*tan (x)^22*sec (x)^4 Show a step by step solution Draw graph Edit expression Direct link to this page Value at x=
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This calculus video tutorial shows you how to find the derivatives if inverse trigonometric functions such as inverse sin^1 2x, tan^1 (x/2) cos^1 (x^2) ta2 4 2k 4k Don't Miss In simple interest what sum amounts of Rs11/in 4 years and Rs10/in 5 years ?2503 · The derivative of tan(2x) is equal to two times the secant squared of two times x Using mathematical notation, the equation is written as d/dx tan(2x) = 2sec^2(2x) The derivative of tan(2x) can be found by using the quotient rule and the chain rule
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First Method y = cot^1(secxtanx) dy/dx = 1/{1(secxtanx)^2} d/dx(secxtanx) dy/dx = 1/{1sec^2xtan^2x2secxtanx}(secxtanxsec^2x)Get an answer for 'Prove that the derivative of tan x is sec^2 x' and find homework help for other Math questions at eNotes$\begingroup$ What's the derivative of $\tan x$?
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1 See answer Vahin8411 is waiting for your help Add your answer and earn pointsDerivative of sec^2x) full pad » x^2 x^ {\msquare} \log_ {\msquare} \sqrt {\square} \nthroot \msquare {\square} \le \ge · The derivative of the function secant squared of x is d/dx(sec^2(x)) = 2sec^2(x)tan(x) This derivative is obtained by applying the chain rule of differentiation and simplifying the result Sec^2(x) is a composite function that can be rewritten as (sec(x))^2
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· From sin 2 x cos 2 x =1, dividing by cos 2 x gives tan 2 x 1 = sec 2 x Thus, another form for the final solution can be written as For the first example, we could writeGet the answers you need, now!Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history
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How do find the derivative of y=(sec)2x(tan)2x?Answer to What is the derivative of tan^2(x)? · If units of degrees are intended, the degree sign must be explicitly shown (eg, sin x°, cos x°, etc) Using this standard notation, the argument x for the trigonometric functions satisfies the relationship x = (180x/π)°, so that, for example, sin π = sin 180° when we take x = π In this way, the degree symbol can be regarded as a
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· Explanation note tan2x = (tanx)2 differentiate using the chain rule given y = f (g(x)) then dy dx = f '(g(x)) × g'(x) ← chain rule y = (tanx)2 ⇒ dy dx = 2tanx × d dx (tanx) ⇒ dy dx = 2tanxsec2x Answer linkDerivative Proofs d/dx tan (x)=sec^2 (x) Watch later Share Copy link Info Shopping Tap to unmute If playback doesn't begin shortly, try restarting your device Up next in 8 · i think your derivative (with brackets) is ok since $\tan(x)$ has a derivative thus $\tan(x)\tan(x)=\tan(x)^2$ has also a derivative and is given by $2\cdot(1\tan(x)^2)(\tan(x))$ (in the range of definition) a comment before the downvoting is starting $$\tan(x)'=\frac{1}{\cos(x)^2}=\frac{\sin(x)^2\cos(x)^2}{\cos(x)^2}=1\tan(x)^2$$
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