Question

Question #f4b5c

Answer 1

`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`