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

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

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

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

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derivative of

y = \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}}

cos (2 x + π)

5 t y^{^{'}} + (10 + 5 t (\frac{2 ( t - 7 )}{7 t})) y = 0

\frac{\partial}{\partial x} (10 sin (x y))

\int (12 x + 7) d x

x \to 4 lim (\frac{1}{x - 3})

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