Question

How many times will the chain rule need to be used to find the derivative of y = cos(sin(3x + 5))?

a) 2
b) 3
c) 4
d) 5

Answer 1

The chain rule needs to be used twice to find the derivative of y = cos(sin(3x + 5)).

Correct option is b.

Step-by-step explanation:

To find the derivative of y = cos(sin(3x + 5)), we need to apply the chain rule multiple times.

First, we differentiate the outer function, which is cos(u), where u = sin(3x + 5). The derivative of cos(u) is -sin(u).

Then, we differentiate the inner function, which is sin(3x + 5). The derivative of sin(u) is cos(3x + 5) * (3), as the derivative of 3x + 5 is 3.

Therefore, we have used the chain rule twice to find the derivative of y = cos(sin(3x + 5)).