Question

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): sinⁿ x

Answer 1

Let y = sinⁿ x.

Accordingly, for n = 1, y = sin x.

For n = 2, y = sin² x.

For n = 3, y = sin³ x.

We assert that

Let our assertion be true for n = k.

i.e.,

Thus, our assertion is true for n = k + 1.

Hence, by mathematical induction,