Differentiate 10sinxcosx

asked May 20, 2021 55.8k views

1 vote

by Jrh

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4 votes

Answer:

$10\,cos\,2x$

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

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