Question

what's the derivative of the square root of ((x^2)*(6^x))^9?

Answer 1

\[\frac{d}{dx}(\sqrt{x^26^x})^9\] like that?

Answer 2

0

Answer 3

the 9 is under the square root

Answer 4

to find the derivative of that.

Answer 5

\[\sqrt{((x^2)*(6^x))^9}\] sorry it's actually this

Answer 6

hey u have to use the rule of partial differentiatio
i.e.,
(d/dx)(x^18*6^9x)

Answer 7

maybe best to write
\[x^2x^6=x^8\] and
\[(x^8)^9=x^{72}\] and
\[\sqrt{x^{72}}=x^{36}\] and take the derivative of that

Answer 8

but because it's 6^x and not x^6 i don't think i can do that

Answer 9

ooooh ok then you have to do something else

Answer 10

\[\sqrt{(x^2\times 6^x)^9}\] like this?

Answer 11

\[\frac{d}{dx}\sqrt{x^{18}6^{9x}}=\frac{1}{2\sqrt{x^{18}6^{9x}}}\times \frac{d}{dx}[x^{18}6^{9x}]\] by the chain rule

Answer 12

then
\[\frac{d}{dx}[x^{18}6^{9x}]=18x^{17}6^{9x}+x^{18}\times 9\times \ln(x)\times 6^{9x}\]

Answer 13

then some algebra to clean it up