Derivatives Find the derivative of the following functions. Se...

Question

Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the derivative of √x.

y = x⁵

Accepted Answer

Hi, everyone. Let's take a look at this practice problem dealing with derivatives. This problem says to find the derivative of the function H of R, which is equal to R rated to the 8th power. We're given 4 possible choices as our answers. For choice A, we have 8 multiplied by R rated to the 8th power. For choice B, we have 7 multiplied by R raised to the 8th power. For choice C, we have 7 multiplied by R raised to the 7th power, and for choice D, we have 8 multiplied by R to the 7th power. Now we need to take the derivative of our function, H of R, which is equal to R rated to the 8th power. We need to take that derivative with respect to R. So we're gonna be looking for H of R. Which is equal to the derivative with respect to R, of the quantity of R rates to the 8th power. And so here we need to recall our power rule for derivatives. That is the derivative with respect to R, of the quantity of R raises to the end. And that's going to be equal to N multiplied by R raised to the N minus 1 power. So here in our case, N is going to be equal to 8. So when we take this derivative, it's going to be equal to 8. Multiplied by R, raised to the 8 minus 1. And 8 minus 1 is 7, so this is going to be equal to 8, multiplied by R raised to the 7th power. So that is the answer that we're looking for. And if we compare this to our answer choices, the correct answer choice corresponds to answer choice D. So I hope that this explanation has been useful, and I'll see you in the next video.

Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the derivative of √x.y = x⁵

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Derivatives Find the derivative of the following functions. See Example 2 of Section 3.2 for the derivative of √x.
y = x⁵