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Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): sin^n x

19.  Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): \sin^ n x

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Given,

f(x)=\sin^ n x

Now, As we know the chain rule of derivative,

[f(g(x))]'=f'(g(x))\times g'(x)

And, the property,

f'(x^n)=nx^{n-1}

Applying those properties, we get

f'(x)=n\sin^ {n-1} x \cos x

Hence Derivative of the given function is n\sin^ {n-1} x \cos x

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