If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Worked example: Derivative of ∜(x³+4x²+7) using the chain rule

Let's tackle the challenge of differentiating the fourth root of a polynomial expression in this worked example. Using the chain rule and the power rule, we simplify the complex function and evaluate the derivative at x=-3. Join us on this mathematical journey!

## Want to join the conversation?

• I think that Sal left out the final step when solving for f'(-3). He finishes with an answer of 3/32 but neglects to multiply this by 3 (from u'(x)). I believe that the correct answer for f'(-3) is 9/32. No? Hopefully this solution wasn't critical to the programming of a manned orbiter, or those astronauts might be in for a fun ride!
• Actually, he multiplied the 3 (from u'(x)) with the 1/4, and thus became 3/4.

So 3/32 is the correct answer
• Shouldn't you be able to distribute the radical and then use the power rule?
f(x) = x^3/4 + 4x^2/4 + 7^1/4f'(x) = 3/4x^(-1/4) + 2x^(-1/2) + 0
(1 vote)
For example: (x + y) ^ 2 = x^2 + 2xy + y^2
This can't be written as x^2 + y^2
• at he says we are working with a composite function, how do we know if we are or not?
• Basically it means if you have a function inside of a function. In the title of the video you have the polynomial starting with x^3 inside of the fourth root. This can also take the form of something like sin(ln(x)) with ln being inside of sin or something like e^sqrt(x) where the square root function is "inside" of e^x. It's a little tricky to spot at first but you get the hang of it with practice.

It may help if you imagine that you are able to replace one part of the function with a g(x) where g(x) equals that function. Let me know if that didn't help.