What is (\partial)/(\partial x)(x^{8/x}) ?

The answer to (\partial)/(\partial x)(x^{8/x}) is 8x^{(8-2x)/x}(-ln(x)+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(x^{8/x})

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

8 x^{\frac{8 - 2 x}{x}} (- ln (x) + 1)

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (\frac{8}{x} ln (x)) = \frac{8 ( - ln ( x ) + 1 )}{x ^{2}}

= e^{\frac{8}{x} l n (x)} \frac{8 ( - ln ( x ) + 1 )}{x ^{2}}

Simplify

e^{\frac{8}{x} l n (x)} \frac{8 ( - ln ( x ) + 1 )}{x ^{2}} : 8 x^{\frac{8 - 2 x}{x}} (- ln (x) + 1)

= 8 x^{\frac{8 - 2 x}{x}} (- ln (x) + 1)

\int \frac{12 x ^{3} - 1}{3 x ^{4} - x + 10} d x

\int \frac{( e ^{x} + e ^{- x} )}{e ^{x} - e ^{- x}} d x

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

3 cos (8 x), 3 - 3 cos (8 x), [0, \frac{π}{8}]

\frac{d}{d x} (\frac{4}{3} x^{3} - 4 x + 3)

What is (\partial)/(\partial x)(x^{8/x}) ?
The answer to (\partial)/(\partial x)(x^{8/x}) is 8x^{(8-2x)/x}(-ln(x)+1)