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## Calculus, all content (2017 edition)

### Course: Calculus, all content (2017 edition)>Unit 2

Lesson 15: Radical functions differentiation (intro)

# Fractional powers differentiation

Sal differentiates h(x)=5x^¼+7, and evaluates the derivative at x=16. This can actually be done quite easily using the Power rule!

## Want to join the conversation?

• Why do you cube 16^(1/4)?
• According to exponent rules, x^(ab) = (x^a)^b. Therefore, 16^(3/4) = 16^(1/4*3) = (16^(1/4))^3.
• At how does Sal know that 16^(1/4) is two. I thought it's 4 in the very first moment ( i know 4 is wrong^^). Should one really be able to do such things with the brain or should one use a trick for calculating it..
• It's quite simple to be honest. Since its one over some 2^n in which n ∈ natural numbers. This means that we're dealing with square roots. If we rearrange it to 16^(1/(2^2)) (which looks complex but if you write it down its not) then we can see that we're just taking the square root two times. So square root of 16 is 4 then square root of 4 is 2