Help with derivatives - step by step

[unique wadi]

You can start off by writing the cube root of 3x^2 as (3x^2)^1/3

$(3x^2)^\frac{1}{3}$

[deft flame]

m64sky

[unique wadi]

then apply the power rule

of a derivative

so it should be (1/3)*(3x^2)^-2/3

$\frac{1}{3}(3x^2)^\frac{-2}{3}$

[deft flame]

m64sky

[unique wadi]

and then you use the chain rule

so u multiply it by the derivative of (3x^2)

which is 6x

$\frac{1}{3(3x^2)^\frac{2}{3}}\cdot6x$

[deft flame]

m64sky

[unique wadi]

Then just simplify it

so you should get this

as your answer

[unique wadi]

.solved

[toxic mesa]

Solved

Post marked as solved by @unique wadi.

Use .unsolved if this was a mistake.

[kind bridge]

(\frac{6x}{3(9x^4)^{\frac{1}{3}}} )

(\frac{2x}{x(9x)^{\frac{1}{3}}} )

(\frac{2}{(9x)^{\frac{1}{3}}} )

[deft flame]

jstN0body

[kind bridge]

We square 3x^2 and multiply by 6x

[deft flame]

jstN0body

[kind bridge]

since we have x^4 we can change that to x^3 * x and take the cube root of x^3 which just leaves x outside of the expression, then also divide 6 by 3

[deft flame]

jstN0body

[kind bridge]

finally just cancel the x terms to get the answer

@halcyon sparrow hope that helps