Question

if tan inverse -1(cotx)find dy /dx​

Answer 1

Concept:

Here, we have applied the concept of differentiation.

Given:

$tan^{-1}cotx$

To find:

The derivative of the function

Solution:

We know that

$tan^{-1} = \frac{1}{tan} \\and \\cotx=\frac{1}{tan}$

So, if we put these values in the function, then we can find the derivative of the given function

Let's assume y to be the function

$y=tan^{-1}cotx$

$y= tan^{-1}cotx\\ y=\frac{1}{tan} \frac{1}{tan} \\ y=\frac{1}{tan^{2}x } \\y=cot^{2} x$

Now, we can differentiate the function y with respect to x

$\frac{dy}{dx}=cot^{2} x\\\frac{dy}{dx}=2cotx(cosec^{2}x)$

∴The derivative of $y=tan^{-1}cotx$ is $2cotx(cosec^{2} x)$

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