Find the derivative of the following function: x⁴(5 sin x - 3 cos x)

Solution:

The given function is f(x) = x⁴ (5 sin x - 3 cos x)

Using the product rule, its derivative is,

d/dx (f(x)) = (5 sin x - 3 cos x) d/dx (x⁴) + x⁴ d/dx (5 sin x - 3 cos x)

= (5 sin x - 3 cos x) (4x³) + x⁴ (5 cos x - 3 (- sin x))   (using derivative formulas)

= x³ (20 sin x - 12 cos x + 5x cos x + 3x sin x)

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 22

Find the derivative of the following function: x⁴ (5 sin x - 3 cos x)

Summary:

The derivative of the given function x⁴ (5 sin x - 3 cos x) is x³ (20 sin x - 12 cos x + 5x cos x + 3x sin x)