Answered: "Use Version 2 of the Chain Rule to..."

compagnia04

Answered question

2021-12-07

Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

y = \sin (4 \cos z)

Hector Roberts

Beginner2021-12-08Added 31 answers

Step 1
Given function is

y = \sin (4 \cos z)

.
To find the derivative of the given functions.
Solution:
Chain rule of differentiation states that:

\frac{d}{d x} [f (g (x))] = f^{'} (g (x)) \cdot g^{'} (x)

Differentiating the given function with respect to z,

\frac{d y}{d z} = \frac{d}{d z} [\sin (4 \cos z)]

= \cos (4 \cos z) \cdot \frac{d}{d z} (4 \cos z)

= \cos (4 \cos z) \cdot 4 (- \sin z)

= - 4 \sin z \cos (4 \cos z)

Step 2
Hence, derivative of the given function is

- 4 \sin z \cos (4 \cos z)

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