Answer:
[tex]10\,cos\,2x[/tex]
Explanation:
To differentiate: [tex]10\,sinx\,\,cos x[/tex]
Solution:
Use product rule: [tex][f(x)g(x)]'=f'(x)g(x)+f(x)g'(x)[/tex] and the following formulae:
[tex](sinx)'=cosx\,,\,(cosx)'=-sinx[/tex]
[tex](10\,sinx\,\,cos x)'=10[(sinx)'cosx+(sinx)(cosx)']\\\\=10[cosx\,cosx-sinx\,sinx]\\\\=10[cos^2x-sin^2x][/tex]
Use [tex]cos^2x-sin^2x=cos2x[/tex]
[tex](10\,sinx\,cosx)'=10\,cos2x[/tex]
