Differential Calculus Problem Example 3

Description:

Problem

Calculate the derivatives of following functions −

f(x) = tan(sin x³)

Solution

f(x) = tan(sin x³), Calculate d/dx(f(x)).

We have to use chain rule for this problem.

Let’s say t = sin x³. Then,

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

Differentiating, and putting t = sin x³ −

sec²(sin x³) × d(sin x³)/dx

Let’s say p = x³. Then,

sec²(sin x³) × d(sin p)/dp × d(p)/dx

Differentiating, and putting p = x³ −

sec²(sin x³) × cos x³ × d(x³)/dx

Hence,

d/dx(f(x)) = 3x²(cos x³) [sec²(sin x³)]