"Determine the Derivatives f(x)=ln⁡[esin⁡h(cot⁡h(sin⁡h(x2)))]" was answered by our experts

Cem Hayes

Answered question

2021-09-27

Determine the Derivatives
$f (x) = \ln [e^{\sin h (\cot h (\sin h (x^{2})))}]$

Brighton

Skilled2021-09-28Added 103 answers

Solution:
Given: The function is

f (x) = \ln [e^{\sin h (\cot h (\sin h (x^{2})))}]

.
Rewrite the function:

f (x) = \sin h (\cot h (\sin h (x^{2})))

Differentiate f with respect to x:

\frac{d}{d x} f (x) = \cos h (\cot h (\sin h (x^{2}))) \frac{d}{d x} (\cot h (\sin h (x^{2})))

= \cos h (\cot h (\sin h (x^{2}))) (- {\csc h}^{2} (\sin h (x^{2}))) \frac{d}{d x} (\sin h (x^{2}))

= - {\csc h}^{2} (\sin h (x^{2})) \cos h (\cot h (\sin h (x^{2}))) \cos h (x^{2}) \frac{d}{d x} (x^{2})

= - {\csc h}^{2} (\sin h (x^{2})) \cos h (\cot h (\sin h (x^{2}))) \cos h (x^{2}) (2 x)

Conclusion:
Therefore, the derivative is

f^{'} (x) = - 2 x {\csc h}^{2} (\sin h (x^{2})) \cos h (\cot h (\sin h (x^{2}))) \cos h (x^{2})

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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