What is the derivative of (cos(x))/(2+sin(x)) ?

The derivative of (cos(x))/(2+sin(x)) is (-sin(x)(2+sin(x))-cos^2(x))/((2+sin(x))^2)

What is the first derivative of (cos(x))/(2+sin(x)) ?

The first derivative of (cos(x))/(2+sin(x)) is (-sin(x)(2+sin(x))-cos^2(x))/((2+sin(x))^2)

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derivative of

\frac{cos ( x )}{2 + sin ( x )}

\frac{- sin ( x ) ( 2 + sin ( x ) ) - cos ^{2} ( x )}{( 2 + sin ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{cos ( x )}{2 + sin ( x )})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

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

Simplify

\frac{( - sin ( x ) ) ( 2 + sin ( x ) ) - cos ( x ) cos ( x )}{( 2 + sin ( x ) ) ^{2}} : \frac{- sin ( x ) ( 2 + sin ( x ) ) - cos ^{2} ( x )}{( 2 + sin ( x ) ) ^{2}}

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

What is the derivative of (cos(x))/(2+sin(x)) ?
The derivative of (cos(x))/(2+sin(x)) is (-sin(x)(2+sin(x))-cos^2(x))/((2+sin(x))^2)
What is the first derivative of (cos(x))/(2+sin(x)) ?
The first derivative of (cos(x))/(2+sin(x)) is (-sin(x)(2+sin(x))-cos^2(x))/((2+sin(x))^2)