1. ## Product Rule Question

Hi,

I'm asked to differentiate $\displaystyle f(x) = 3(x^2 + 2)(4x^2 - 5x^4) - 3$.

Using the product rule, I know that $\displaystyle f'(x) = u'v + uv'$.

What I'm confused about, is what to set $\displaystyle u$ and $\displaystyle v$ to in the above function. Would $\displaystyle u=3(x^2 + 2)(4x^2 - 5x^4)$and $\displaystyle v = -3$?

Thanks,

2. Originally Posted by centenial
Hi,

I'm asked to differentiate $\displaystyle f(x) = 3(x^2 + 2)(4x^2 - 5x^4) - 3$.

Using the product rule, I know that $\displaystyle f'(x) = u'v + uv'$.

What I'm confused about, is what to set $\displaystyle u$ and $\displaystyle v$ to in the above function. Would $\displaystyle u=3(x^2 + 2)(4x^2 - 5x^4)$and $\displaystyle v = -3$?

Thanks,
No, not at all.

u and v are functions of x.

Since the derivative of a constant is zero, you can forget about the -3 at the end.

Also the multiplier 3 can be used as simply an external factor.

Hence

$\displaystyle u(x)=x^2+2$

$\displaystyle v(x)=4x^2-5x^4$

$\displaystyle \frac{d}{dx}\left[3\left(x^2+2\right)\left(4x^2-5x^4\right)-3\right]=3\frac{d}{dx}\left[\left(x^2+2\right)\left(4x^2-5x^4\right)\right]$

You could of course just multiply out the expression and differentiate term by term also.

3. Originally Posted by centenial
Hi,

I'm asked to differentiate $\displaystyle f(x) = 3(x^2 + 2)(4x^2 - 5x^4) - 3$.

Using the product rule, I know that $\displaystyle f'(x) = u'v + uv'$.

What I'm confused about, is what to set $\displaystyle u$ and $\displaystyle v$ to in the above function. Would $\displaystyle u=3(x^2 + 2)(4x^2 - 5x^4)$and $\displaystyle v = -3$?

Thanks,
product rule ...

$\displaystyle u = 3(x^2+2)$

$\displaystyle v = (4x^2-5x^4)$

the -3 term at the end of the expression is inconsequential since the derivative of -3 is 0

4. Thanks! I think I understand now.