Power rule and product rule problem

[footprints]

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

 

[courtrigrad]

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

 

[footprints]

Ok. Thanks!

 

[footprints]

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

 

[arildno]

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!