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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

\frac{d}{d x} ((3 x^{2} + 1)^{4})

k = 1 \sum \infty \frac{k ^{3}}{3 ^{k}}

y^{^{'}} + 3 y = 2 e^{- 3 x}

y = x^{3} - x, (- 1, 0)

f (x) = \frac{2}{x}, at x = - 1

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