If $f(x)= - x^2 + x$ and $g(x) = sqrtx + x$ , how do you differentiate $f(g(x))$ using the chain rule?

Question

If $f(x)= - x^2 + x$ and $g(x) = sqrtx + x$ , how do you differentiate $f(g(x))$ using the chain rule?

1 Answer

Impact of this question

1889 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-17T02:50:03

$-1-2sqrt(x)-x/sqrt(x)-2x$

Explanation:

Assuming you already know the chain rule. If not:
Given $h(x)$ is a composite function consisting of 2 functions such that $h(x)=f(g(x))$ , $h'(x)=f'(g(x))g'(x)$ .

So, in this scenario, $f'(x)=-2x$ and $g'(x)=1/(2(sqrt(x)))+1$
Substitute $g(x)$ into $f'(x)$ :
$-2(sqrt(x)+x)$
And multiply by $g'(x)$ :
$-2(sqrt(x)+x)*(1/(2sqrt(x))+1)$
$-2(1/2+sqrt(x)+x/(2sqrt(x))+x)$
$-1-2sqrt(x)-x/sqrt(x)-2x$

Science

Math

Humanities

... and beyond

If $f(x)= - x^2 + x$ and $g(x) = sqrtx + x$ , how do you differentiate $f(g(x))$ using the chain rule?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

If f(x)= - x^2 + x f(x)= - x^2 + x and g(x) = sqrtx + x g(x) = sqrtx + x , how do you differentiate f(g(x)) f(g(x)) using the chain rule?

1 Answer

Explanation:

Related questions

Impact of this question

If $f(x)= - x^2 + x$ and $g(x) = sqrtx + x$ , how do you differentiate $f(g(x))$ using the chain rule?