What is the derivative of x^v ?

The derivative of x^v is x^v(ln(x)(dv)/(dx)+v/x)

What is the first derivative of x^v ?

The first derivative of x^v is x^v(ln(x)(dv)/(dx)+v/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} (x^{v})

x^{v} (ln (x) \frac{d v}{d x} + \frac{v}{x})

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{v} = e^{v l n (x)}

= \frac{d}{d x} (e^{v l n (x)})

Apply the chain rule:

e^{v l n (x)} \frac{d}{d x} (v ln (x))

= e^{v l n (x)} \frac{d}{d x} (v ln (x))

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

= e^{v l n (x)} (ln (x) \frac{d v}{d x} + \frac{v}{x})

e^{v l n (x)} = x^{v}

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

\int \frac{1 + x + x ^{2}}{x} d x

\int \frac{ln ( x )}{x ^{a}} d x

\int \frac{( 3 x ^{2} + 2 )}{x - 1} d x

\int sin (3 x) sin (k x) d x

\int (3 x - 4)^{7} d x

What is the derivative of x^v ?
The derivative of x^v is x^v(ln(x)(dv)/(dx)+v/x)
What is the first derivative of x^v ?
The first derivative of x^v is x^v(ln(x)(dv)/(dx)+v/x)