What is the derivative of ln(xcsc(x)) ?

The derivative of ln(xcsc(x)) is (csc(x))/x-cot(x)csc(x)ln(x)

What is the first derivative of ln(xcsc(x)) ?

The first derivative of ln(xcsc(x)) is (csc(x))/x-cot(x)csc(x)ln(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} (ln (x) csc (x))

\frac{csc ( x )}{x} - cot (x) csc (x) ln (x)

Solution steps

\frac{d}{d x} (ln (x) csc (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = ln (x), g = csc (x)

= \frac{d}{d x} (ln (x)) csc (x) + \frac{d}{d x} (csc (x)) ln (x)

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

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

Simplify

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

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

y^{^{'}} = - 5 sin (3 t) + 2 cos (4 t)

x \to 0 lim (\frac{1}{sin ( 5 x )})

y = - x^{2} + 16, x = - 2, y = 0, x = 3

x \to 4 + lim (\frac{4}{x - 4})

\int e^{2 - 3 x} d x

What is the derivative of ln(xcsc(x)) ?
The derivative of ln(xcsc(x)) is (csc(x))/x-cot(x)csc(x)ln(x)
What is the first derivative of ln(xcsc(x)) ?
The first derivative of ln(xcsc(x)) is (csc(x))/x-cot(x)csc(x)ln(x)