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

The derivative of (x^x/(sin(x))) is x^xcsc(x)(ln(x)+1)-x^xcot(x)csc(x)

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

The first derivative of (x^x/(sin(x))) is x^xcsc(x)(ln(x)+1)-x^xcot(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{x ^{x}}{sin ( x )})

x^{x} csc (x) (ln (x) + 1) - x^{x} cot (x) csc (x)

Solution steps

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

Simplify

\frac{x ^{x}}{sin ( x )} : x^{x} csc (x)

= \frac{d}{d x} (x^{x} csc (x))

Apply the Product Rule:

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

f = x^{x}, g = csc (x)

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

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

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

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

Simplify

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

a sin (\frac{t}{c})

\int x^{\frac{1}{3}} sin (x^{\frac{4}{3}} + 8) d x

x \to 0 + lim (\frac{1}{x} - \frac{1}{e ^{x} - 1})

\frac{d}{d x} (e^{c o s (x) - 2 s e c (x)})

\frac{d ^{3}}{d x ^{3}} (- sin (3 x))

What is the derivative of (x^x/(sin(x))) ?
The derivative of (x^x/(sin(x))) is x^xcsc(x)(ln(x)+1)-x^xcot(x)csc(x)
What is the first derivative of (x^x/(sin(x))) ?
The first derivative of (x^x/(sin(x))) is x^xcsc(x)(ln(x)+1)-x^xcot(x)csc(x)