Question

Find the derivative of (x^4)*(3-9x)^(1/2)

Answer 1

I know that the power rule has to be used, and I think the chain rule, but I'm still not the greatest at the latter. :/

Answer 2

I know that the derivative of x^4 = 4x^3...

Answer 3

The derivative of (3-9x)^(1/2) = 1/2 (3-9x)^(-1.2), I think...

Answer 4

you are going to take lots of derivatives
so first off just memorize this:
\[\frac{d}{dx}\sqrt{x}=\frac{1}{2\sqrt{x}}\]
it never changes, so forget about using the power rule with \(\frac{1}{2}\) just straight up remember it. that way when your classmates are all converting to exponents, using the power rule, and converting back, you are already done. like memorizing seven times eight

Answer 5

I still don't have 7*8 memorized. xD But, I'll make sure to memorize that, it just helps.

Answer 6

so by the chain rule, the derivative of
\[\sqrt{3-9x}\] is
\[\frac{1}{2\sqrt{3-9x}}\times (-9)=\frac{-9}{2\sqrt{3-9x}}\]

Answer 7

yeah i know, that is why i use seven times eight as an example
all the others everyone knows, that you just have to memorize

Answer 8

of course for
\[x^4\sqrt{3-9x}\] you need both the product rule and the chain rule

Answer 9

So, it would be the derivative of\[x^4\sqrt{3-9x} * \frac{ -9 }{ 2\sqrt{3x-9} }\] ; not the ddrivative of the whole thing, I just the first function * what was all ready found out

Answer 10

Chain rule is mind boggling business.

Answer 11

you will also need to use the product rule.

Answer 12

f = x^4
f' = 4x^3
g= (3-9x)^1/2
g' = -9/2(sqrt (3-9x)
f'*g+g'*f

Answer 13

Thanks, I'll see what I can do from there. :)