Question

Differentiate 10sinxcosx​

Answer 1

`10\,cos\,2x`

Step-by-step explanation:

To differentiate:
`10\,sinx\,\,cos x`

Solution:

Use product rule:
`[f(x)g(x)]'=f'(x)g(x)+f(x)g'(x)` and the following formulae:

`(sinx)'=cosx\,,\,(cosx)'=-sinx`

`(10\,sinx\,\,cos x)'=10[(sinx)'cosx+(sinx)(cosx)']\\\\=10[cosx\,cosx-sinx\,sinx]\\\\=10[cos^2x-sin^2x]`

Use
`cos^2x-sin^2x=cos2x`

`(10\,sinx\,cosx)'=10\,cos2x`