# How do you find the derivative of #u=(x^2+3x+1)^4#?

##### 3 Answers

You have two options: The first is to expand that polynomial and take the derivative. The other is to do a substitution to get the solution:

#### Explanation:

I'm going to go with the second option, because I'm not a masochist (jokes!)

When you take a derivative of a set of terms in parentheses, you can do a substitution, treating the parentheses as a separate single function. We'll treat the in-parentheses terms like this:

so our function now looks like this:

Now, the derivative is not simply

if

Re-inserting our substitutions, we now arrive at our answer:

#### Explanation:

Use the chain and power rule. Find the derivative of

#### Explanation:

#"differentiate using the "color(blue)"chain rule"#

#"Given "y=f(g(x))" then"#

#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#

#u=(x^2+3x+1)^4#

#rArr(du)/dx=4(x^2+3x+1)^3xxd/dx(x^2+3x+1)#

#color(white)(rArr(du)/dx)=4(2x+3)(x^2+3x+1)^3#