Question

Can someone help me find the derivative of the problem below? I'll give a medal! :)

Answer 1

\[\frac{ 5 }{ (2x)^3 }\]

Answer 2

do you want to use quotient rule or product rule?

personally I think product rule is easier xD

Answer 3

Whatever you think is easier, I'm okay with.

Answer 4

mmmkk

well do you know product rule? :)
\[\frac{ d }{ dx } [f(x) * g(x)] ~~=~~ f(x)*g'(x) + g(x)*f'(x)\]right? :)

Answer 5

Yes, I am familiar with it

Answer 6

mmm
I'm not awake

we can rewrite the given equation as
\[5*(2x)^{-3}\]right?

Answer 7

Yes

Answer 8

turns out we don't need product rule xD (cuz the numeator is a constant...)
ingore what me said before

we use power rule and chain rule
\[5*(2x)^{-3} \rightarrow 5(-3)*(2x)^{-4}*(\frac{ d }{ dx }2x)\]

Answer 9

tell me if you get confused xD

Answer 10

Sorry, my page keeps reloading.
And that makes sense

Answer 11

You'd get -30(-2x)^4

Answer 12

-30(2x)^4
sorry the 2s not negative

Answer 13

mhmm then we simplify
and get
\[-15 * (2x)^{-4} * (2) \rightarrow -30 * (2x)^{-4} \rightarrow \frac{ -30 }{ (2x)^{4} } \]\(\huge \rightarrow \frac{-30}{16x^4} \rightarrow \frac{-15}{8x^4}\)

Answer 14

you can also just use power rule...
if you write
\[5(2x)^{-3} =5(2)^{-3}x^{-3} =\frac{5}{2^3}x^{-3}=\frac{5}{8}x^{-3} \\ \text{ then differentiate using power rule }\]

Answer 15

yay math
thanks @freckles :)

Answer 16

Thank you, both of you. :)

Answer 17

glad we could helppp :)