Question

How do you use the chain rule to differentiate `sin(e^(6x))`?

Answer 1

`6e^(6x) cos(e^(6x))`

Explanation:

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

`color(red)(|bar(ul(color(white)(a/a)color(black)(dy/dx=dy/(du)xx(du)/(dx))color(white)(a/a)|)))........(A)`

`rArry=sin(e^(6x))`

let `color(blue)(u=e^(6x))rArr(du)/dx=e^(6x).d/dx(6x)=6e^(6x)`

and `y=sincolor(blue)(u)rArr(dy)/(du)=coscolor(blue)(u)`

substitute these values into (A) converting u into terms of x

`rArrdy/dx=cosu.6e^(6x)=6e^(6x)cos(e^(6x))`