The derivative of tan x - x with respect to x | vedclass

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Question

(D) Let $f(x) = 	an x - x$. To find the derivative with respect to $x$,we differentiate both terms: $\frac{d}{dx}(	an x - x) = \frac{d}{dx}(	an x)

Vedclass · Accepted Answer

$	an^2 x$

Vedclass · Answer

(D) Let $f(x) = 	an x - x$. To find the derivative with respect to $x$,we differentiate both terms: $\frac{d}{dx}(	an x - x) = \frac{d}{dx}(	an x) - \frac{d}{dx}(x)$. We know that $\frac{d}{dx}(	an x) = \sec^2 x$ and $\frac{d}{dx}(x) = 1$. Therefore,$f'(x) = \sec^2 x - 1$. Using the trigonometric identity $1 + 	an^2 x = \sec^2 x$,we have $\sec^2 x - 1 = 	an^2 x$. Thus,the derivative is $	an^2 x$.

The derivative of $\tan x - x$ with respect to $x$ is

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