Question

find the derivative of (2x+1)ln(x^2+5)

Answer 1

Oh my goodness... I've been spending the past 5 minutes trying to solve the integral... It's just a derivative.. Oh I'm silly :3 ok ok ok let's see.

Looks like we'll need to start with the product rule.

Answer 2

is it (fg)'= f' g + f g' ?

Answer 3

Ah sorry I got distracted for a few minutes there D:
Yes very good c:

Answer 4

\[\large \frac{d}{dx}(2x+1)\ln(x^2+5)=\]
\[\large \color{royalblue}{\frac{d}{dx}(2x+1)}\ln(x^2+5)+(2x+1)\color{royalblue}{\frac{d}{dx}\ln(x^2+5)}\]

Ok understand the setup? we need to take the derivative of the blue pieces.

Answer 5

i understand that and got up until the derivative ln(x^2+5). i don't understand how to get that

Answer 6

Do you know the derivative of \(\ln x\)?

Answer 7

1/x?

Answer 8

yes, good.
We'll do the same thing here, but we'll have to be careful about what our `x` is.
And we'll also need to apply the chain rule.

Here's a quick silly example just in case the concept is a little confusing.

Answer 9

Whatever the `argument` is (the thing inside of the log), that entire contents gets put into the bottom.
Then we apply the chain rule, multiplying by the derivative of the inner function.

Answer 10

BAHHH my pictured got messed up, there should be a prime on that far right potato.