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

The derivative of (cot(x)/(1-sin(x))) is (csc(x)(cot^2(x)-csc(x)))/(1-csc(x))

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

The first derivative of (cot(x)/(1-sin(x))) is (csc(x)(cot^2(x)-csc(x)))/(1-csc(x))

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

\frac{csc ( x ) ( cot ^{2} ( x ) - csc ( x ) )}{1 - csc ( x )}

Solution steps

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

\frac{d}{d x} (cot (x)) = - csc^{2} (x)

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

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

Simplify

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

= \frac{csc ( x ) ( cot ^{2} ( x ) - csc ( x ) )}{1 - csc ( x )}

\frac{d}{d x} (sin (8 x) e^{4 x})

ln (x^{2} - 4)

\int sin (x) (- 8 x cos (2 x)) d x

x \to 0 lim (3 x + 2)

f (x) = \frac{2}{3 x}

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