en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^{8x}

Solution

derivative of

x^{8 x}

Solution

8 x^{8 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (x^{8 x})

Apply exponent rule:

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

x^{8 x} = e^{8 x l n (x)}

= \frac{d}{d x} (e^{8 x l n (x)})

Apply the chain rule:

e^{8 x l n (x)} \frac{d}{d x} (8 x ln (x))

= e^{8 x l n (x)} \frac{d}{d x} (8 x ln (x))

\frac{d}{d x} (8 x ln (x)) = 8 (ln (x) + 1)

= e^{8 x l n (x)} \cdot 8 (ln (x) + 1)

e^{8 x l n (x)} = x^{8 x}

= 8 x^{8 x} (ln (x) + 1)

Popular Examples

integral from-infinity to-3 of 4/(x^5)

\int_{- \infty}^{- 3} \frac{4}{x ^{5}} d x

integral of+x^9sqrt(x^5+7)

\int + x^{9} x^{5} + 7 d x

derivative of (2.99*10^{16})/(r^2)derivative of

\frac{2.99 \cdot 1 0 ^{16}}{r ^{2}}

(\partial)/(\partial y)(xy^2e^{-xz})

\frac{\partial}{\partial y} (x y^{2} e^{- x z})

(\partial)/(\partial y)(x^6-8x^5y)

\frac{\partial}{\partial y} (x^{6} - 8 x^{5} y)

Frequently Asked Questions (FAQ)

What is the derivative of x^{8x} ?
The derivative of x^{8x} is 8x^{8x}(ln(x)+1)
What is the first derivative of x^{8x} ?
The first derivative of x^{8x} is 8x^{8x}(ln(x)+1)