Math Help - derivatives

1. derivatives

find dy/dx for

2. Originally Posted by algebra2
find dy/dx for
First of all, remember that a square root is a power of $\frac{1}{2}$.

You have a product of functions, so use the product rule.

$\frac{dy}{dx} = (2x+1)^{\frac{1}{2}}\times \frac{d}{dx} (x^3) + x^3 \times \frac{d}{dx}[(2x+1)^{\frac{1}{2}}]$.

To work out the second of the derivatives, use the chain rule.

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

for here, do i multiply the 3x^2 into the (2x+1)^(1/2) to get (6x+3x)^(5/2)?

4. Originally Posted by algebra2
$(2x+1)^{\frac{1}{2}}\times (3x^2)$ $
$

for here, do i multiply the 3x^2 into the (2x+1)^(1/2) to get (6x+3x)^(5/2)?
No, just write it as $3x^2(2x+1)^{\frac{1}{2}}$.