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

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

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

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

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derivative of

f (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 )}

\int \frac{2 x ^{3} + 3 x ^{2} - 4}{x ^{2} - 4 x + 3} d x

\frac{d}{d z} (sin^{2} (z))

\frac{2}{s ^{2} + s - 2}

\frac{( s + 1 )}{s ^{2} + 2 s + 5}

\int \frac{6 t - 15}{3 t ^{2} - 2} d t

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