Question

How do you differentiate `cos(x^4)-2sinx`?

Answer 1

`-4x^3sin(x^4)-2cosx`

Explanation:

Using `color(blue)"standard derivatives"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(sinx)=cosx,d/dx(cosx)=-sinx)color(white)(2/2)|)))`

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

`• d/dx[cos(f(x))]=-sin(f(x))xxf'(x)`

`rArrd/dx[cos(x^4)-2sinx]`

`=-sin(x^4)xxd/dx(x^4)-2cosx`

`=-4x^3sin(x^4)-2cosx`