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Chesley

Answered question

2021-10-12

Find the derivatives of the functions defined as

y = \cos (4 e^{2 x})

Answer & Explanation

Obiajulu

Skilled2021-10-13Added 98 answers

Step 1
Given information:
The function is

y = \cos (4 e^{2 x})

.
Concept used:
Chain rule of differentiation:

\frac{d}{d x} (p (q (x))) = p^{'} (x) q^{'} (x)

\frac{d}{d x} (e^{a x}) = a e^{a x}

\frac{d}{d x} (\cos x) = - \sin x

Step 2
Now find the derivative of the function

y = \cos (4 e^{2 x})

by the use of chain rule of differentiation.

\frac{d}{d x} (\cos (4 e^{2 x})) = - \sin (4 e^{2 x}) \frac{d}{d x} (4 e^{2 x})

= - \sin (4 e^{2 x}) \cdot 8 e^{2 x}

= - 8 e^{2 x} \sin (4 e^{2 x})

Answer:

\frac{d}{d x} (\cos (4 e^{2 x})) = - 8 e^{2 x} \sin (4 e^{2 x})

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