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Alborosie
2 years ago
15

Differentiate 10sinxcosx​

Biology
1 answer:
Harman [31]2 years ago
8 0

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

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