differentiate question

**decoy808** · February 18th 2010, 04:10 AM

$<br /> y=\sqrt{x^3} (x+1)<br />$

dy/dx = $(x^3){^\frac{1}{3}}+1$

$<br /> \frac{1}{3}x^\frac{-1}{2}<br />$

im unsure about this can anyone help or correct me? many thanks

**danielomalmsteen** · February 18th 2010, 05:38 AM

$y=x^{\frac{2}{3} +1} + x^{\frac{2}{3}}$

then

$y'=\left(\frac{2}{3} +1 \right)\cdot x^{\frac{2}{3} +1 -1} + \left(\frac{2}{3}\right)\cdot x^{\frac{2}{3}-1}$

**NRS** · February 18th 2010, 05:51 AM

First of all,

is not correct, x cubed will be to the one half power, because you are taking the square root of it, not the cube root.

To differentiate, you multiply ((x^3)^(1/2)) and x^(1) to get

(x^3)^(3/2) + 1

Now, differentiate:

dy/dx = (3/2)(x^3)^(1/2)*(3x^2)

**HallsofIvy** · February 18th 2010, 06:06 AM

You also appear not to have "distributed":

$y= \sqrt{x^3}(x+1)= x^{3/2}(x+1)= x^{5/2}+ x^{3/2}$

Now, use that the derivative of $x^n$ is $nx^{n-1}$ .

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differentiate question

Youre going to have to use the chain rule

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