Question

help? step by step

Find dy/dx

Answer 1

\[y=(12\sqrt[3]{x}-\frac{ 1 }{ 4x }+e^2)\]

Answer 2

I know I should rewrite it out..
12*x^(1/3)
but now I'm stuck..?

Answer 3

\[\sqrt[3]{x} = x^(\frac{ 1 }{ 3 }\]

by the property, you subtract 1. So 1/3 - 1 = ?
\[\frac{ 1 }{ 4x } = \frac{ 1 }{ 4 }x^{-1} \]

and \[e^2 \]
is just a constant.

Answer 4

\[x^{\frac{ 1 }{ 3 }}\]

Answer 5

okay, thanks.

Answer 6

\[y' = \frac{ 4 }{ x^{\frac{ 2 }{ 3 } }} - \frac{ 1 }{ 4x^2 }\]

Answer 7

so.. rewritten it's \[(12*x^{1/3}-\frac{ 1 }{ 4 }x^{-1}+e^2)\]

Answer 8

sorry, change the - to +.

Answer 9

ahhh i messed up on the original equation

Answer 10

\[(12\sqrt[3]{x}-\frac{ 1 }{ 4x }+e^2)^7\]

Answer 11

so it's chain rule right?

Answer 12

It's the same thing. now you apply chain rule.

Answer 13

\[7(4x^{\frac{ -2 }{ 3 }} + \frac{ 1 }{ 4x^2 })^6\]

Answer 14

mm.. the answer is different then that.

Answer 15

\[7(12\sqrt[3]{x}-\frac{ 1 }{ 4x }+e^2)^6(4x^{-2/3}+\frac{ 1 }{4 }x^{-2})\]

Answer 16

oh yeah, you multiply by the deriv again.

Answer 17

why do you multiply by the derivative?

Answer 18

oh nevermind haha

Answer 19

I got it.

Answer 20

I'm forgetting my simple rulessss! Ahhhh D;

Answer 21

chain rule states f'(g(x))*g'(x)

Answer 22

it's all good, i totally 4got chain rule for a moment. im rusty in my math

Answer 23

thanks so much though ;D

Answer 24

i remember the chain rule by ths

let u equal some function within a function

and y=\[f(u)\]

so you have\[y=f(u)\]

\[\frac{dy}{dx}=\frac{du}{dx}\frac{dy}{du}\] if you remember one party like du/dx or dy/du.... you'll know what you ned to cancel