Chain Rule for Derivatives: Differentiating a Product with Chain Rule

[mg0stisha]

Homework Statement

Differentiate $$f(x)=(3x^{2}+4)^{3}(5-3x)^{4}$$

Homework Equations

N/A

The Attempt at a Solution

I can see that this derivative is a product, yet also involves using chain rule. With this being said, am i just supposed to evaluate these separately using chain rule for each then multiply the results together? Or is there another way to differentiate this? Thanks in advance.

 

[Pengwuino]

Take it as $$f(x) = g(u(x))h(v(x))$$. Then $$f'(x) = g'(u)h(v) + h'(v)g(u)$$ where for example $$g'(u) = \frac{dg(u)}{dx} = \frac{dg(u)}{du}*\frac{du}{dx}$$, your standard chain rule.

 

[mg0stisha]

Ah yes I see it now, thank you very much!

 

[fghtffyrdmns]

This is a product rule question, however, to take the derivative of this, you'll need the derivative of first and the derivative of the 2nd, thus the chain rule.

If you don't want to use the chain rule, you can expand both and use the product rule. :)