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

$\dfrac{1}{1+cos x}$

Calculus 1 / AB

Chapter 3

Derivatives

Section 5

Derivatives of Trigonometric Functions

Differentiation

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this question asked us to find the derivative of sign of X over one plus co sign of X. And since this is a fraction, we have to use the quotient rule, which could be outlined in the red on the right hand side. So to begin, I'm going to define our G and act terms. So where G term is always what's in the denominator? So that's one place clue. Sign it X, and the derivative of this equals minus sign effects, and our effort backs is whatever is in the numerator. So in this case, it's sign of X, and the derivatives is co sign of X. So now we can plug these terms into this formula here so we'll get who sign of X Times one plus come sign of x waas sign of X Say my bad. This is a negative minus sign of X times minus sign of X, all over one plus co sign of X squared. So to start off, we're going to want to distribute this co sign possible terms here and because we have two negatives being multiplied together, that adds, or that multiplies to eat positive. So when we multiply we then get co sign of X close Co signed squared of X plus sine squared of X all over one plus co sign of Ax squared and Our Triggered. And he says that when these two are present, the equal one. So now we have co sign of X Plus one over one plus cu Sign of X Square and notice how these air the same terms in the numerator and the denominator so we can cancel or numerator with one of the terms and denominator to get 1/1 plus co sign of X.

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