Question #f4b5c

1 Answer
Jim G.
Oct 9, 2016

#f'(x)=1/x sinx+cosxln5x#

Explanation:

Differentiate using the #color(blue)"product rule"#

If # f(x)=g(x).h(x)" then"#

#color(red)(bar(ul(|color(white)(a/a)color(black)(f'(x)=g(x)h'(x)+h(x)g'(x))color(white)(a/a)|))) #

here #g(x)=sinxrArrg'(x)=cosx#

differentiate h(x) using the #color(blue)"chain rule"#

#h(x)=ln(5x)rArrh'(x)=1/(5x).d/dx(5x)=5/(5x)=1/x#
#"--------------------------------------------------------------------------"#

#rArrf'(x)=sinx xx1/x+ln5x xxcosx#

#=1/xsinx+cosxln5x#

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