How can I go about differentiating (3x^2)/((x-4)^(2/3)) ? I think I have the answer, but I am not completely sure.

Question

revircs · Answer

For clarification: $$\frac{ 3x^2 }{ (x-4)^{2/3} }$$

solomonzelman · Answer

you can re-write it as:

$\large\color{black}{ \displaystyle (3x^2)((x-4)^{-2/3}) }$

and then apply the product rule.

solomonzelman · Answer

what is the derivative of:

[1]       $\large\color{black}{ \displaystyle 3x^2 }$

[2]      $\large\color{black}{ \displaystyle (x-4)^{-2/3} }$

revircs · Answer

1) 6x
2) $$-2/3(x-4)^{-5/3}$$

revircs · Answer

and after the product rule, it would be (6x) ((x-4)^(-2/3) + (3x^2)(-2/3(x-4)^(-5/3)

solomonzelman · Answer

yes, that is right!

revircs · Answer

simplified, it would be $$6x(x-4)^{-2/3}-\frac{ 6x^2 }{ 3(x-4)^{5/3} }$$ is this the complete differentiation?