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}}

t^{3} cos (t)

\int \frac{1}{x ^{4} + x} d x

x \to 0 lim (\frac{( 2 - x ) ^{2} - 4}{x})

x^{3} - x, 3 x

\frac{\partial}{\partial x} (x^{2} sin^{2} (y))

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)