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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{1}{1 + cos ( x )}

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= - (- csc^{2} (x)) - cot (x) csc (x)

Simplify

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

= \frac{1}{1 + cos ( x )}

y^{^{'}} + \frac{3 x}{x ^{2} + 4} y = \frac{x}{x ^{2} + 4}, y (0) = 1

y = 4 x^{2}, y = 7 x - 3 x^{2}

\frac{2 x}{2 + x}

\int sin^{2} (8 x) d x

\frac{d}{d x} (5 x^{4} - 60 x^{2} + 64)

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