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# Find the derivative of the following function (where n is an integer): sinⁿx

**Solution:**

The given function is f(x) = sin^{n}x.

It can be written as

f(x) = sin x sin x sin x ... sin x *(n times)*.

Using the product rule, its derivative is,

d/dx (f(x)) = [ sin x sin x ... sin x *(n-1) times *d/dx (sin x)

+ sin x sin x ... sin x *(n-1) times *d/dx (sin x)

+ ... + sin x sin x ... sin x *(n-1) times *d/dx (sin x) ] *(n times)*

= sin x sin x ... sin x *(n-1) times *[ cos x + cos x + ... + cos x *(n times)*]

= sin^{n-1} x [n cos x]

= n sin^{n-1}x cos x

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 19

## Find the derivative of the following function (where n is an integer): sinⁿx

**Summary:**

The derivative of the given function sinⁿx is n sin^{n-1}x cos x

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