Question

What is the value of `(f*g)'` if `f(u)=u^2, u=g(x)=x^5+2, x=1`?

Answer 1

`color(green)(30)`

Explanation:

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

`(f*g)(x)` (personally, I prefer the equivalent `f(g(x))` notation)
`color(white)("XXX")=g(x)^2`
`color(white)("XXX")=(x^5+2)^2`
`color(white)("XXX")=x^10+4x^5+4`

The derivative, `(f*g)'(x) = 10x^9+20x^4`

At `x=1`
`color(white)("XXX")(f*g)'(1)=10xx1^9+20xx1^4=30`