Answer to Question #238359 in Economics of Enterprise for Gemma Cayapes

Question

let f(x) = (6x+3) and g(x)=(-2x+5)

*use chain rule to calculate h'(x) where h(x)=f(g(x)

Answer 1

Given that$f(x)=(6x+3)$ and $g(x)=(-2x+5)$ , we can find $h'(x)$ , where $h(x)=f(g(x))$

Now,

$h(x)=f(g(x)).........................................(1)$

Differentiate (1) with respect to x using chain rule we get

$h'(x)=\frac{d}{dx}[f(g(x))]$

$=f'(g(x)).g'(x)...........................................(2)$

Now f'(g(x) is the derivative of f with x replaced by g, this can be written as $\frac{df}{dg}$

Now,

$f(x)=(6x+3)$

so

$f'(x)=\frac{d}{dn}(6x+3)=6$

so

$f'(g(x))=6$

And

$g(x)=(-2x+5)$

so

$g'(x)=\frac{d}{dn}(-2x+5)$

$=-2$

so from (2)

$h'(x)=6\times-2=-12$