# Thread: Need help with a few derivatives

1. ## Need help with a few derivatives

Hi,

I'm given 3 functions I need to find f' of:

f(x) = x(3x-9)^3

f(x) = x√(2x+3)

f(x) = t^2
√(t-2)

You're supposed to use the chain rule for these, but I run into a problem. For example, the second function. I start by changing the equation to x(2x+3)^1/2, I multiply x by the exponent (1/2), subtract 1 from the exponent, and then multiply by the derivative (2) to finish with x(2x+3)^-1/2. But that doesn't give the right answer. Actually, I managed to get every other problem on the assignment correct except for these ones that have a variable multiplied by a polynomial. Could anyone tell me what I've done wrong?

Thanks!

2. ## Re: Need help with a few derivatives

So what you did was just treat the first "x" as a constant? That, of course, is wrong. Use the product rule.
The derivative of $\displaystyle x(3x- 9)^3$ is $\displaystyle (3x- 9)^2+x(3(3x- 9)^2(3))$.

Another way to do this is to move the "x" into the rest of the function: $\displaystyle f(x)= x(3x- 9)^3= (x^{1/3}(3x- 9))^3= (3x^{4/3}- 9x^{1/3})^3$.

3. ## Re: Need help with a few derivatives

Originally Posted by KevinShaughnessy
Hi,
I'm given 3 functions I need to find f' of:
f(x) = x√(2x+3)
$\displaystyle x\sqrt{2x+3}$ is a product.

Here is the back-of-the-book answer: $\displaystyle \sqrt{2x+3}+\frac{x^2}{\sqrt{2x+3}}$

Can you explain why?

4. ## Re: Need help with a few derivatives

Awesome, I see where I went wrong now. Thanks a lot guys.