What is the derivative of x^{{p}(x}) ?

The derivative of x^{{p}(x}) is x^{{p}(x)}(ln(x) derivative of {p}(x)+({p}(x))/x)

What is the first derivative of x^{{p}(x}) ?

The first derivative of x^{{p}(x}) is x^{{p}(x)}(ln(x) derivative of {p}(x)+({p}(x))/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^{p (x)})

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

w

\int x^{3} x d x

x \to 3 + lim (4 - x^{2})

\frac{d}{d x} (a \cdot x + ln (x))

x \cdot \frac{d y}{d x} = 6 y

What is the derivative of x^{{p}(x}) ?
The derivative of x^{{p}(x}) is x^{{p}(x)}(ln(x) derivative of {p}(x)+({p}(x))/x)
What is the first derivative of x^{{p}(x}) ?
The first derivative of x^{{p}(x}) is x^{{p}(x)}(ln(x) derivative of {p}(x)+({p}(x))/x)