What is the derivative of (cos(x)/(2sin^2(x))) ?

The derivative of (cos(x)/(2sin^2(x))) is (-sin^3(x)-sin(2x)cos(x))/(2sin^4(x))

What is the first derivative of (cos(x)/(2sin^2(x))) ?

The first derivative of (cos(x)/(2sin^2(x))) is (-sin^3(x)-sin(2x)cos(x))/(2sin^4(x))

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

\frac{- sin ^{3} ( x ) - sin ( 2 x ) cos ( x )}{2 sin ^{4} ( x )}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (sin^{2} (x)) = sin (2 x)

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

Simplify

\frac{1}{2} \cdot \frac{( - sin ( x ) ) sin ^{2} ( x ) - sin ( 2 x ) cos ( x )}{( sin ^{2} ( x ) ) ^{2}} : \frac{- sin ^{3} ( x ) - sin ( 2 x ) cos ( x )}{2 sin ^{4} ( x )}

= \frac{- sin ^{3} ( x ) - sin ( 2 x ) cos ( x )}{2 sin ^{4} ( x )}

\frac{d}{d x} (e^{\frac{1}{x}})

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

\int (e^{x} - x^{e} + \frac{5}{x}) d x

\int 4^{7 x} d x

x \to - 1 lim (x + 5 - 2)

What is the derivative of (cos(x)/(2sin^2(x))) ?
The derivative of (cos(x)/(2sin^2(x))) is (-sin^3(x)-sin(2x)cos(x))/(2sin^4(x))
What is the first derivative of (cos(x)/(2sin^2(x))) ?
The first derivative of (cos(x)/(2sin^2(x))) is (-sin^3(x)-sin(2x)cos(x))/(2sin^4(x))