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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

\frac{d}{d x} (x cos (y))

\int_{0}^{10} 2200 e^{0.024 x} - 1460 e^{0.018 x} d x

\int \frac{1}{T} d T

n = 1 \sum \infty \frac{1}{n - 1}

\frac{1 - 4 t}{1 + 3 t}

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