How do you differentiate #f(x)=xsinx+cosx#?

1 Answer
Jim G.
Mar 9, 2017

#f'(x)=xcosx#

Explanation:

#color(orange)"Reminder"#

#• d/dx(sinx)=cosx" and " d/dx(cosx)=-sinx#

#"to differentiate "xsinx" use the "color(blue)"product rule"#

#"Given "f(x)=g(x)h(x)" then"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(f'(x)=g(x)h'(x)+h(x)g'(x))color(white)(2/2)|)))larr" product rule"#

#"here "g(x)=xrArrg'(x)=1#

#"and "h(x)=sinxrArrh'(x)=cosx#

#rArrf'(x)=xcosx+sinxlarr" derivative of "xsinx#

Differentiating the original f(x)

#f(x)=xsinx+cosx#

#rArrf'(x)=xcosx+sinx-sinx#

#rArrf'(x)=xcosx#

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