Question

Find the derivative of
`F(x) = e^{cos^(2)(3x)}` using any applicable rules.

Answer 1

`f(x)=e^(\cos^2(3x))\\\\\\f'(x)=e^(\cos^2(3x))\cdot2\cos(3x)\cdot(-\sin (3x))\cdot 3\\\\f'(x)=-6e^(\cos^2(3x))\sin(3x)\cos (3x)`

Answer 2

`f(x)=e^(\cos^2(3x))\\\\f'(x)=\left(e^(\cos^2(3x))\right)'=e^(\cos^2(3x))\cdot2\cos(3x)\cdot(-\sin(3x))\cdot3\\\\=-3e^(\cos^2(3x))2\sin(3x)\cos(3x)=-3e^(\cos^2(3x))\sin(2\cdot3x)\\\\=-3e^(\cos^2(3x))\sin(6x)\\\\Used:\\\\(e^x)'=e^x\\\\\left(f(g(x))\right)'=f'(g(x))\cdot g'(x)\\\\(x^n)'=nx^(n-1)\\\\\sin(2x)=2\sin x\cos x`