# How do you differentiate #f(x)=x^2(x+7)^3# using the product rule?

##### 2 Answers

#### Explanation:

Product rule: if

In this case, too differentiate terms "A" and "B", we have to use the chain rule.

Now simplify by factoring:

# :. f'(x) = x(x+7)^2 (5x+14} #

#### Explanation:

If you are studying maths, then you should learn the Product Rule for Differentiation, and practice how to use it:

# d/dx(uv)=u(dv)/dx+v(du)/dx # , or,# (uv)' = (du)v + u(dv) #

I was taught to remember the rule in words; "*The first times the derivative of the second plus the second times the derivative of the first* ".

So with

# :. d/dx(uv) = u(dv)/dx+v(du)/dx #

# :. f'(x) = (x^2)(3(x+7)^2) + ((x+7)^3)(2x) #

# :. f'(x) = 3x^2(x+7)^2 + 2x(x+7)^3 #

# :. f'(x) = x(x+7)^2 {3x+2(x+7)} #

# :. f'(x) = x(x+7)^2 (3x+2x+14} #

# :. f'(x) = x(x+7)^2 (5x+14} #