Find the value of differentiated function Let f(x)=cos⁡[cot−1(cos⁡x1−cos⁡2x)] where π4&lt;x&lt;π2 ,then what is the value of d(f(x))d(cot⁡(x))?

Get the answer to "Find the value of differentiated function Let f(x)=cos⁡[cot−1(cos⁡x1−cos⁡2x)]..."

Jamya Elliott

2022-01-29

Find the value of differentiated function
Let

f (x) = \cos [\cot^{- 1} (\frac{\cos x}{\sqrt{1 - \cos 2 x}})]

where

\frac{π}{4} < x < \frac{π}{2}

,then what is the value of

\frac{d (f (x))}{d (\cot (x))}

primenamaqm

Beginner2022-01-30Added 12 answers

You need not apply the chain rule. As you have already solved upto the following step,

f (x) = \cos (\cot^{- 1} (\frac{\cot x}{\sqrt{2}}))

(Note that I have corrected your calculation mistake and written 2–√ instead of 2)
Now, let

\cot x = y

, given function becomes,

\cos (\cot^{- 1} (\frac{y}{\sqrt{2}}))

\cos (\cot^{- 1} (x)) = \frac{x}{\sqrt{x^{2} + 1}}

Now the function reduces to

\frac{y}{\sqrt{y^{2} + 2}}

and you can differentiate it easily.

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?