Question

find the nth derivative of sin^7 x cos ^5 x ??​

Answer 1

Step-by-step explanation:

derivation of this will be

= 5cos5x-7sin7x

hope it helps you｡◕‿◕｡

Answer 2

The derivative of the equation = 7sin^6x × cosx × cos^5x - 5cos^4x × sinx × sin^7x

Here, the y = u × v derivative formula is applied.

where, u = sin^7x   and   v = cos^5x

Hence,

(dy/dx) = u × (dv/dx) + v × (du/dx)

= sin^7x × (5cos^4x × -sinx) + cos^5x × (7sin^6x × cosx)

= 7sin^6x × cosx × cos^5x - 5cos^4x × sinx × sin^7x