# Math Help - chain rule

1. ## chain rule

find dy/dx

y=xto3(5xto2 =1)to-2/3

2. (5xto2 = 1) represents $(5x^2 ? 1)$
What is the operation?

3. ok the answer in the book is 1/3xto2(5xto2 +1)to-5/3 (25x + 9)

I started the problem like this
-3xto2(5xto2 +1)to-5/3 (10x)

do am I on the right track?

4. You need to use the product rule to compute the derivative.

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

Let $u = x^3$ and $v = (5x^2 + 1)^{-2/3}$.

Then the derivative of the function uv is:

$u \cdot \frac{dv}{dx} + v \cdot \frac{du}{dx}$.

Can you calculate $\frac{du}{dx}$ and $\frac{dv}{dx}$?

5. so it will be like this?

(xto3)-2/3(10x)to-5/3 + (5xto2 +1)to-2/3(3xto2)

6. Originally Posted by homerb
so it will be like this?

(xto3)-2/3(10x)to-5/3 + (5xto2 +1)to-2/3(3xto2)
The right side of your equation is correct, but the left is not.

7. that is where I have problems. can you show me how it is done