If y = sec(tan^{-1} x),then frac{dy}{dx} at x | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given $y = \sec(	an^{-1} x)$.Using the chain rule,we differentiate with respect to $x$:$\frac{dy}{dx} = \sec(	an^{-1} x) \cdot 	an(	an^{-1} x)

Vedclass · Accepted Answer

$\frac{1}{\sqrt{2}}$

Vedclass · Answer

(C) Given $y = \sec(	an^{-1} x)$.Using the chain rule,we differentiate with respect to $x$:$\frac{dy}{dx} = \sec(	an^{-1} x) \cdot 	an(	an^{-1} x) \cdot \frac{d}{dx}(	an^{-1} x)$$\frac{dy}{dx} = \sec(	an^{-1} x) \cdot x \cdot \frac{1}{1+x^2}$Since $	an^{-1} x = 	heta$,then $	an 	heta = x$,which implies $\sec 	heta = \sqrt{1+x^2}$.Substituting this into the derivative:$\frac{dy}{dx} = \sqrt{1+x^2} \cdot x \cdot \frac{1}{1+x^2} = \frac{x}{\sqrt{1+x^2}}$Now,evaluating at $x = 1$:$\left. \frac{dy}{dx} ight|_{x=1} = \frac{1}{\sqrt{1+1^2}} = \frac{1}{\sqrt{2}}$.

If $y = \sec(\tan^{-1} x)$,then $\frac{dy}{dx}$ at $x = 1$ is equal to

Similar Questions

If the vectors $a \hat{i}+\hat{j}+\hat{k}$,$\hat{i}+b \hat{j}+\hat{k}$,and $\hat{i}+\hat{j}+c \hat{k}$ $(a \neq 1, b \neq 1, c \neq 1, a \neq b \neq c)$ are coplanar,then the value of $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ is:

Which of the following is a genetically dominant trait in human beings?

Which one of the following is a secondary alcohol?

$\lim _{x \rightarrow \infty}\left(\frac{x+6}{x+1}\right)^{x+4}$ is equal to

Beats are produced by two waves given by $y_1 = a \sin(2000 \pi t)$ and $y_2 = a \sin(2008 \pi t)$. The number of beats heard per second is

Vedclass Test Series

Exam Paper Generator

Online Exam Module