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# Differentiate the function.$S(p) = \sqrt{p} - p$

## $$S^{\prime}(p)=\frac{1}{2} p^{-1 / 2}-1 \text { or } \frac{1}{2 \sqrt{p}}-1$$

Derivatives

Differentiation

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

Hey, it's clear zone. You're in here so you have us of P is equal to well squared of T minus P, which is equal to P to the one have power minus P. We could differentiate both sides with respect to pee, so we get D over a DP Pete's. The one have Power Dynasty over dp p, and we apply the power roll to get 1/2 p. It's in one P to the 1/2 minus one minus one. And when we simplify, we get one over two square root P minus one.

#### Topics

Derivatives

Differentiation

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp