Question

Find the derivative of the given function.

Answer 1

Explanation:

In photo below

Subject : Mathematics

Level : College

Chapter : Calculus (Differentials)

Answer 2

`2x\;sin^7x + 7x^2sin^6x\;cos\;x + (1)/(cos^(6)x) + (6xsin\;x)/(cos^(7)x)`

Explanation:

`y = x^2 sin^7x + x\;cos^(-6)x\\\\(dy)/(dx) = (d)/(dx)(x^2 sin^7x + x\;cos^(-6)x )\\\\= (d)/(dx)(x^2 sin^7x) + (d)/(dx)(x\;cos^(-6)x )\\\\=sin^7x(d)/(dx)(x^2) + x^2(d)/(dx)(sin^7x) + cos^(-6)x(d)/(dx)(x) + x(d)/(dx)(cos^(-6)x)\\\\=(sin^7x)(2x) + x^2(7sin^6x)(cos\;x) + cos^(-6)x + x(-6cos^(-7)x)(-sin\;x)\\\\=2x\;sin^7x + 7x^2sin^6x\;cos\;x + cos^(-6)x + 6xsin\;x\;cos^(-7)x\\\\=2x\;sin^7x + 7x^2sin^6x\;cos\;x + (1)/(cos^(6)x) + (6xsin\;x)/(cos^(7)x)`