en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^{2*x}

Solution

derivative of

x^{2 \cdot x}

Solution

2 x^{2 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (x^{2 x})

Apply exponent rule:

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

x^{2 x} = e^{2 x l n (x)}

= \frac{d}{d x} (e^{2 x l n (x)})

Apply the chain rule:

e^{2 x l n (x)} \frac{d}{d x} (2 x ln (x))

= e^{2 x l n (x)} \frac{d}{d x} (2 x ln (x))

\frac{d}{d x} (2 x ln (x)) = 2 (ln (x) + 1)

= e^{2 x l n (x)} \cdot 2 (ln (x) + 1)

e^{2 x l n (x)} = x^{2 x}

= 2 x^{2 x} (ln (x) + 1)

Popular Examples

derivative of 6x^{-2}derivative of

6 x^{- 2}

derivative of sin^3(3x^7-2x+i)

\frac{d}{d x} (sin^{3} (3 x^{7} - 2 x + i))

derivative of (2x)/((x^2+1))derivative of

\frac{2 x}{( x ^{2} + 1 )}

derivative of y=(x^4+5x^2)^7 derivative of

y = (x^{4} + 5 x^{2})^{7}

derivative of y-x^2+1 derivative of

y - x^{2} + 1

Frequently Asked Questions (FAQ)

What is the derivative of x^{2*x} ?
The derivative of x^{2*x} is 2x^{2x}(ln(x)+1)
What is the first derivative of x^{2*x} ?
The first derivative of x^{2*x} is 2x^{2x}(ln(x)+1)