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Numerade Educator

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Problem 31 Easy Difficulty

Differentiate the function.
$ z = \frac {A}{y^{10}} + Be^y $

Answer

$$z^{\prime}=-10 A y^{-11}+B e^{y}=-\frac{10 A}{y^{11}}+B e^{y}$$

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Video Transcript

So for this problem, we're asked to differentiate. The function and the function were given is ah function of why the function is e. So it's Z equals, uh, a over 10 y or a over right to the 10th. So a over y 2/10 and then it's going to be plus B E to the y. So with differentiation, we know that we can take each portion of the some, um and then add those derivatives up separately. So Z Prime is going to equal first the derivative of this, plus the derivative. This the way we can write this, which would make it a lot easier for us, is a Y to the negative. 10th. That way, it's much easier to differentiate. We don't have to use the the quotient role, so we'll bring our negative 10 out in front a. Why. And then it's going to be now to the negative 11th because we subtract one. Explain it. Another way we could do this, though, would be to put this underneath y to the 11th, so it's in the similar form, and then lastly, what we'll do is add be we know each other, why it's derivative is just each of the Y on. We would use change role to differentiate the exponents, but we're differentiating with respect to why so it'll just stay like this. Now we have our final differentiated form of the function.