Question

Can someone explain to me why the answer is 3cos3x (it has something to do with chain rule i think)

Answer 1

Use the fundamental theorem of calculus. It says that

`\displaystyle(\mathrm d)/(\mathrm dx)\int_{\text{constant}}^(g(x))f(t)\,\mathrm dt=f(g(x))\cdot(\mathrm dg)/(\mathrm dx)`

In this case,
`g(x)=3x` and
`f(t)=\cos t`. Then

`\displaystyle(\mathrm d)/(\mathrm dx)\int_0^(3x)\cos t\,\mathrm dt=\cos(3x)\cdot(\mathrm d)/(\mathrm dx)3x=3\cos3x`