Question

If f(x)=x^3+3x^2+4x+5 and g(x)=5x then what is d/dx g(f(-1))?

Answer 1

See below.

Explanation:

I'm not absolutely sure what you are asking here. `g(f(-1))` would be a constant, and therefore its derivative would be `0`. I will do the problem as I think it should be.

If `f(x)=x^3+3x^2+4x+5` and `g(x)=5x`

Then:

`g(f(x))=5(x^3+3x^2+4x+5)=5x^3+15x^2+20x+25`

`dy/dxg(f(x))=dy/dx(5x^3+15x^2+20x+25)=15x^2+30x+20`

Plugging in `x=-1`

`15(-1)^2+30(-1)+20=color(blue)(5)`