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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

Take the constant out:

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial v} (4 u sin (v))

\int x x - 15 d x

\int x e^{x y} d y

\int e^{x + 1} d x

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

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