Differential Calculus Problem Example 2

Description:

Problem

Calculate the derivatives of following functions −

f(x) = sin(cos x)

Solution

f(x) = sin(cos x), Calculate d/dx(f(x)).

Let’s say t = cos x.

Hence, f(x) = sin(cos x) can be written as, f(t) = sin(t)

Hence,

d/dx(f(x)) = d(f(t))/dt × dt/dx = d(sin(t))/dt × dt/dx

Differentiating, and putting t = cos x −

cos(cos x) × d(cos x)/dx

Hence,

d/dx(f(x)) = -sin x cos(cos x)