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Find the derivatives of the given functions.$$p=\frac{1}{\sin s}+\frac{1}{\cos s}$$

$\frac{d p}{d s}=-\cot s \csc s+\tan s \sec s$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 1

Derivatives of the sine and Cosine Functions

Derivatives

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02:18

Okay. We want to find you. I. D. X. Or Y equals one over sine X plus one over coast sex. So to do so we're going to rely on driven shortcuts. We picked up through a single variable. Help specifically Rule 0 to 3. Here relevant rules are zero D. D. X. And expose Cossacks. Dd expose expos native syntax rules 123 other powerful product will in general, respectively. We're going to rely on rule 01 and three to solve this. So first, let me write Y in a form that's easier to differentiate. This is why I will sign Xnegative Firstplus Cossacks negative. First from this, we can use the chain rule combined with rule zero to solve So from this we have the truth as follows. Dy reacts equals Cossacks over Science Great X minus negative Sine X over two square X. This simplifies to the solution on the right, but rather in the bottom signed QB X minus coast few decks over Science squared expo square decks. The way that we obtain the solution from the left is by multiplying the left term by Coast Grade Extra Coast Grade X and the right term by Science Grade Extra Science Grade X. Combining our denominators. Thus, we have signed cubed X minus coast cubic science squared X. Coast Guard X.

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