"Calculating derivatives Find the derivative of the following..." was answered by our experts

BenoguigoliB

Answered question

2021-10-18

Calculating derivatives Find the derivative of the following functions.

y = \frac{1 - \cos x}{1 + \cos x}

Answer & Explanation

tabuordg

Skilled2021-10-19Added 99 answers

Step 1
to find the derivative we will use the quotient rule which says

\frac{d y}{d x} = \frac{v \frac{d u}{d x} - u \frac{d v}{d x}}{v^{2}}

here

v = 1 + \cos x and u = 1 - \cos x

\Rightarrow \frac{d v}{d x} = - \sin x and \frac{d u}{d x} = \sin x

Step 2
substituting the values in the formula we get

\frac{d y}{d x} = \frac{(1 + \cos x) (\sin x) - (1 - \cos x) (- \sin x)}{{(1 + \cos x)}^{2}}

\frac{d y}{d x} = \frac{(1 + \cos x) (\sin x) + (1 - \cos x) (\sin x)}{{(1 + \cos x)}^{2}}

\frac{d y}{d x} = \frac{\sin x [1 + \cos x + 1 - c i s x]}{{(1 + \cos x)}^{2}}

\frac{d y}{d x} = \frac{2 \sin x}{{(1 + \cos x)}^{2}}

Jeffrey Jordon

Expert2022-03-13Added 2605 answers

Answer is given below (on video)

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