Question

calculus @solomonzelman

Answer 1

derivative of...

Answer 2

Should I pull out the exponent 2 first?

Answer 3

product and chain rule

Answer 4

you can if you did (sqrt6 x)^2

Answer 5

\(\color{#000000 }{ \displaystyle 4x^5\ln(6x^2) }\)
\(\color{#000000 }{ \displaystyle 8x^5\ln(6x) }\)
\(\color{#000000 }{ \displaystyle 8x^5\ln(x)+8\ln(6)x^5 }\)

Answer 6

i would just use chain rule directly if it was me

Answer 7

So, the second part is just power-rule, and first is just product...
There are several ways to do the problem, tho'.

Answer 8

or like solo just did use log property of product

Answer 9

Oh, right...anyway, would the derivative of \(\large \ln(6x^2) = 2\Large \frac{1}{x^2}\)

Answer 10

sorry, ignore the set up there, I was solving in my head as I was typing the LaTeX

Answer 11

no x^2 at bottom is not good

Answer 12

\(\color{#000000 }{ \displaystyle \ln(6x^2)=\frac{1}{6x^2}\times \left[\frac{d}{dx}~6x^2\right] }\)

Answer 13

using the chain rule.

Answer 14

Ah, so 2/x?

Answer 15

precisely;)

Answer 16

yes

Answer 17

Thank you both!

Answer 18

welcome

Answer 19

Just to verify, if you want, you can post the final answer for check.

Answer 20

or, you can check it through wolf..