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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Simplify

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

= \frac{d}{d x} (\frac{1}{x} - csc (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1}{x}) - \frac{d}{d x} (csc (x))

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

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

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

Simplify

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

\frac{d y}{d x} = \frac{6 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

x \to 0 + lim (- x)

\int sec (x) tan (x) - 6 e^{x} d x

y^{^{'}} = 5 (y - t^{2})

x y^{^{'}} + 2 y + x = 1

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