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

**Solution:**

The given function is f(x) = x^{4 }(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 (x^{4}) + x^{4} d/dx (5 sin x - 3 cos x)

= (5 sin x - 3 cos x) (4x^{3}) + x^{4} (5 cos x - 3 (- sin x)) (using derivative formulas)

= x^{3} (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 x^{3} (20 sin x - 12 cos x + 5x cos x + 3x sin x)

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