What is the derivative of (cos(x)/(1+sin(x))) ?

The derivative of (cos(x)/(1+sin(x))) is -1/(1+sin(x))

What is the first derivative of (cos(x)/(1+sin(x))) ?

The first derivative of (cos(x)/(1+sin(x))) is -1/(1+sin(x))

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

- \frac{1}{1 + sin ( x )}

Solution steps

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

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

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

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

Simplify

\frac{( - sin ( x ) ) ( 1 + sin ( x ) ) - cos ( x ) cos ( x )}{( 1 + sin ( x ) ) ^{2}} : - \frac{1}{1 + sin ( x )}

= - \frac{1}{1 + sin ( x )}

\frac{d x}{d y} = \frac{y}{2}

\int x^{2} cos (2 x) d x

\int 9 x^{2} + 4 x - 7 d x

\frac{\partial}{\partial z} (ln (x^{2} + y^{2} + z^{2}))

\frac{\partial}{\partial x} (x^{8} y^{5} - x^{7} y^{4})

What is the derivative of (cos(x)/(1+sin(x))) ?
The derivative of (cos(x)/(1+sin(x))) is -1/(1+sin(x))
What is the first derivative of (cos(x)/(1+sin(x))) ?
The first derivative of (cos(x)/(1+sin(x))) is -1/(1+sin(x))