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

The derivative of (cos(x)/(cos(x)+1)) is -(sin(x))/((cos(x)+1)^2)

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

The first derivative of (cos(x)/(cos(x)+1)) is -(sin(x))/((cos(x)+1)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{x ^{2} + x + 1}{2 x}

\int \frac{8 x}{8 x + 3} d x

\frac{d}{d x} ((7 - 3 x^{3})^{2})

\int_{0}^{2} x e^{- x} d x

x \to 0 lim ((x - 2) e^{- \frac{1}{x}})

What is the derivative of (cos(x)/(cos(x)+1)) ?
The derivative of (cos(x)/(cos(x)+1)) is -(sin(x))/((cos(x)+1)^2)
What is the first derivative of (cos(x)/(cos(x)+1)) ?
The first derivative of (cos(x)/(cos(x)+1)) is -(sin(x))/((cos(x)+1)^2)