Find and simplify the derivative of the following functions.

Question

f(x) = 3x^-9

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 Y, which is equal to 4 multiplied by Y rated to the minus 5 power, and express it in its simplest form. We're given 4 possible choices as our answers. For choice A, we have -20 divided by Y rate to the 6. For choice B, we have 20 divided by Yrate to the 6th. For choice C, we have -20 divided by Y rates to the 4th, and for choice D, we have 20 divided by Y rated to the 4th. Now we're asked to find a derivative of a function H of Y, and we're going to be taking that derivative with respect to Y. We're gonna be looking for H of Y. And that's gonna be equal to the derivative with respect to Y. Of the quantity of 4 multiplied by Y raised to the minus 5 power. Now, in order to take a derivative of this function, we're going to have to recall our constant multiple and power rule for derivatives. So recall for those rules that we're going to have the derivative with respect to Y. Of the quantity of C multiplied by Y raised to the power N. And this is going to be equal to C multiplied by N, multiplied by Y raised to the power of N minus 1. So, if we look at our rule here, we can identify 4 with C and minus 5 with N. And so that means that our derivative is going to be equal to 4 multiplied by minus 5. Multiplied by Y raised to the -5, -1. So, simplifying this expression, this is going to be equal to -20, since we have 4 multiplied by -5, which is going to be -20, and that's gonna be multiplied by Y, raised to the minus 6 power. Since -5 minus 1 gives me minus 6. Now, we can actually rewrite our Y raised to the -6 power as one divided by Y rated to the 6, that means that this is going to be equal to -20, divided by Y raised to the 6th. So this is the answer that we are looking for, and when we compare our answer to our answer choices, the correct answer choice corresponds to answer choice A. So I hope that this explanation has been useful, and I'll see you in the next video.

Find and simplify the derivative of the following functions.f(x) = 3x-9

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Find and simplify the derivative of the following functions.
f(x) = 3x^-9