Question

Integrate f'(g (5x)) g'(5x)

Answer 1

more info, or is that it?

Answer 2

Let h(x) = f(g(5x))

Answer 3

if we compute h ' (x), we get

h(x) = f(g(5x))

h ' (x) = f ' (g(5x)) * g ' (5x) * 5 ... use chain rule twice

h ' (x) = 5f ' (g(5x)) * g ' (5x)

so h ' (x) is very close to what we're given, which is f'(g (5x)) g'(5x). The only difference really is that 5 out front for h ' (x).

Answer 4

\[\Large h^{\prime}(x) = 5f^{\prime}(g(5x))*g^{\prime}(5x)\]

\[\Large \frac{1}{5}h^{\prime}(x) = f^{\prime}(g(5x))*g^{\prime}(5x)\]

\[\Large \int\frac{1}{5}h^{\prime}(x)dx = \int f^{\prime}(g(5x))*g^{\prime}(5x)dx\]

I'm sure you see what to do from here.