Problem

Find the derivative of the following functions. $…

01:40

Problem 30 Hard Difficulty

Find the derivative of the following functions.
$$y=\frac{1-\sin x}{1+\sin x}$$

Answer

Related Courses

Calculus 1 / AB

Calculus Early Transcendentals

Chapter 3

Derivatives

Section 5

Derivatives of Trigonometric Functions

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Video Transcript

we are looking for the derivative of why is equal to one minus sign of X over one plus Scient affects to know Tate. We're looking for a derivative. It will look like D over DX of why is equal to D over DX of one minus sign of X over one plus cited of x to solve for this derivative. We want to use the quotient rule. If over, G prime is equal to f prime times tree minus g prime times f all of this over g squared. To apply this rule, it will look like D over DX Oh, one minus sign of X, both supplied by one plus sign of X minus D over DX multiplied by one plus sign of X well supplied by one minus sign of X. All of this is over G squared, which is one plus sign FX squared. To break down this derivative, we will first find the derivative of one minus sign of X D over DX of one minus side of X. To find this, we're going to use thesis, um difference Rule F plus minus G. Crime is equal to F prime plus minus G prime. So this will look like D over DX if one minus D over DX of side effects, so are derivative. Do you ever t x of one is equal to zero? The derivative D over DX of sign of X is equal to co sign of X applying be some difference rule. It will look like zero minus co sign of X, which is equal Teoh Negative Co sign of X The next derivative we're looking for is D over DX of one plus sign of X. Again, we're going to apply be some difference Rule R D over DX of one plus D over DX of sign of acts so derivative of one is equal to zero While the derivative of sign of X is equal to co sign of X plying the some difference rule we get zero plus co sign of X, which is equal Teoh Co sign of X So now we are going to put everything together. We will get negative co sign of X well supplied by one plus sign of X minus Post sign of X multiplied by one minus sign if x All of this is over. RG squared, which is one plus sign of X squared to simplify, we will get negative to co sign of X over one plus sign of X squared.

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