Given y = tan1 (sin x cos x)/(cos x – sin x) Divide numerator and denominator by cos x y = tan1 (tan x 1)/(1 = tan1 tan (π/4 x) = (π/4 x) dy/dx = 1 Hence option (3) is the answer Was this answer helpful?WBJEE 09 If y=tan1 √(1sin x/1sin x), then the value of (dy/dx) at x=(π/6) is (A) (1/2) (B) (1/2) 1 (D) 1 Check Answer and Solution fExercise Set 33 121 49 y = 1 / tan x = cot x, dy/dx =csc 2 x 50 y = (tan1 x)1, dy/dx =(tan1 x)2 1 1 x 2 51 dy dx = e x x
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Find dy/dx of ,y=1/sin(2x/1x^2) Ask questions, doubts, problems and we will help youWatch Video in App This browser does not support the video element 33 k 800 AnswerFind {eq}\displaystyle \frac{dy}{dx} {/eq} for {eq}\displaystyle y = x tan^ {1} (4 x) {/eq} Rules in Differentiation Different rules in differentiation is applied whenever appropriate Some of
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Solve the differential equation (1x^2) dy/dx y = tan^1 x Updated On 251 To keep watching this video solution for FREE, Download our App Join the 2 Crores Student community now!So y=f((2x1)/(x²1)) Differentiating wrt x this you'll get Dy/dx={f'((2x1)/(x²1))X (x²1)(2)(2x 1)(2x)}/{x²1} Use the derivative of tan^1 and the chain rule The derivative of tan^1x is 1/(1x^2) (for "why", see note below) So, applying the chain rule, we get d/dx(tan^1u) = 1/(1u^2)*(du)/dx In this question u = 2x, so we get d/dx(tan^1 2x) = 1/(1(2x)^2)*d/dx(2x) = 2/(14x^2) Note If y = tan^1x, then tany = x Differentiating implicitly gets us sec^2y dy/dx = 1," " so dy/dx = 1/sec^2y
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