What is the derivative of x^{9/x} ?

The derivative of x^{9/x} is 9x^{(9-2x)/x}(-ln(x)+1)

What is the first derivative of x^{9/x} ?

The first derivative of x^{9/x} is 9x^{(9-2x)/x}(-ln(x)+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (x^{\frac{9}{x}})

9 x^{\frac{9 - 2 x}{x}} (- ln (x) + 1)

Solution steps

\frac{d}{d x} (x^{\frac{9}{x}})

Apply exponent rule:

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

x^{\frac{9}{x}} = e^{\frac{9}{x} l n (x)}

= \frac{d}{d x} (e^{\frac{9}{x} l n (x)})

Apply the chain rule:

e^{\frac{9}{x} l n (x)} \frac{d}{d x} (\frac{9}{x} ln (x))

= e^{\frac{9}{x} l n (x)} \frac{d}{d x} (\frac{9}{x} ln (x))

\frac{d}{d x} (\frac{9}{x} ln (x)) = \frac{9 ( - ln ( x ) + 1 )}{x ^{2}}

= e^{\frac{9}{x} l n (x)} \frac{9 ( - ln ( x ) + 1 )}{x ^{2}}

Simplify

e^{\frac{9}{x} l n (x)} \frac{9 ( - ln ( x ) + 1 )}{x ^{2}} : 9 x^{\frac{9 - 2 x}{x}} (- ln (x) + 1)

= 9 x^{\frac{9 - 2 x}{x}} (- ln (x) + 1)

\frac{d y}{d t} = 2100 - 300 (\frac{y}{17000})

\int \frac{5}{x ^{6}} d x

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

x \to 0 lim (\frac{x ^{2} + 2 x - 1}{x})

1 - x^{2}

What is the derivative of x^{9/x} ?
The derivative of x^{9/x} is 9x^{(9-2x)/x}(-ln(x)+1)
What is the first derivative of x^{9/x} ?
The first derivative of x^{9/x} is 9x^{(9-2x)/x}(-ln(x)+1)