# Power rule and product rule problem

#### footprints

$$(2x+3)^3(x-4)$$
How do I differentiate this?

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Use the product rule: $vdu + udv$. For the first function use the power rule: $x^n = nx^{n-1} \frac{du}{dx}=(3(2x+3)^2(2)$

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Ok. Thanks!

#### footprints

$$\frac{dy}{dx}=3(2x+3)^2(2) + 1$$
Right?

#### arildno

Homework Helper
Gold Member
Dearly Missed
No!
You must be more careful!
Define:
$$f(x)=(2x+3)^{3},g(x)=(x-4)$$
Then,
$$y(x)=f(x)g(x),y'(x)=f'(x)g(x)+f(x)g'(x)$$
You need therefore to calculate f'(x) and g'(x)

#### footprints

I got it! Thank you!