Question

Calculate the derivative of the function.
f(x) = square root of 3x + x^2

Answer 1

\[f(x) = \sqrt{x + x^2}\]
Is this right?

Answer 2

no i entered it into webassign and it says incorrect

Answer 3

I was asking if that was the question.

Answer 4

oh no, its the square root of 3x+x^2 so \[\sqrt{3x+x^2}\]

Answer 5

Yeah, thats what I meant, forgot that silly 3 :P
\[f'(x)=\frac{2x+3}{2\sqrt{x(x+3)}}\]

Answer 6

Can you show the steps or at least how you got the answer? The square root just confuses me

Answer 7

Use the modified chain rule:
\[\frac{d\sqrt u}{du}\frac{du}{dx}\]
with:
u= x^2+3x
d(u^(1/2))/du = 1/(2(u^(1/2)))
We then have:

\[\frac{\frac{d}{dx}(x^2+3x)}{2\sqrt{x^2+3x}}\]
\[=\frac{2x+3}{2\sqrt{x(x+3)}}\]

Answer 8

Oh I see. Thank you!