Question

Find the derivative of the function.
F(t) = e^(8t sin 2t)

Answer 1

We'll use that:


`g(x)=e^(f(x))\\\\ g'(x)=f'(x)e^(f(x))`

So:


`f(t)=e^(8t\sin(2t))\\\\ f'(t)=[8t\sin(2t)]'e^(8t\sin(2t))\\\\ f'(t)=[(8t)'\sin(2t)+8t(\sin(2t))']e^(8t\sin(2t))\\\\ f'(t)=[8\sin(2t)+8t(2\cos(2t))]e^(8t\sin(2t))\\\\ \boxed{f'(t)=8(\sin(2t)+2t\cos(2t))e^(8t\sin(2t))}`