Get the solution to "Compute the following derivatives ddx[sin⁡x1+cos⁡x]"

Tobias Ali

Answered question

2021-05-21

Compute the following derivatives

\frac{d}{d x} [\frac{\sin x}{1 + \cos x}]

Isma Jimenez

Skilled2021-05-22Added 84 answers

Step 1
To find the derivatives
Step 2

(\frac{d}{d x}) (\frac{\sin x}{1 + \cos x})

Differentiating with respect to x then

y^{'} \frac{(1 + \cos x) \times \cos x - \sin x (- \sin x)}{{(1 + \cos x)}^{2}}

Since, used quotient rule

{(\frac{u}{v})}^{'} = \frac{v u^{'} - u v^{'}}{v^{2}}

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

Since,

\sin^{2} x + \cos^{2} x = 1

so,

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

y^{'} = {(1 + \cos x)}^{1 - 2}

Since,

\frac{x^{a}}{x^{b}} = x^{a - b}

y^{'} = {(1 + \cos x)}^{- 1}

y^{'} = \frac{1}{1 + \cos x}

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