Question

Differentiate 10sinxcosx​

Answer 1

Answer:

$10\,cos\,2x$

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 $cos^2x-sin^2x=cos2x$

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