Question

Question #c4bd2

Answer 1

`f'(x)=-sin(lnx)/x`

Explanation:

differentiate using the `color(blue)"chain rule"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(f(g(x)))=f'(g(x))xxg'(x))color(white)(2/2)|)))`

`rArrd/dx(cos(lnx))=-sin(lnx)xxd/dx(lnx)`

`color(white)(rArrd/dx(cos(lnx)))=-sin(lnx)xx1/x`

`color(white)(rArrd/dx(cos(lnx)))=-sin(lnx)/x`