What is the derivative of y=(x+5)^{1/x} ?

The derivative of y=(x+5)^{1/x} is (-(ln(x+5))/(x^2)+1/(x(x+5)))(x+5)^{1/x}

What is the first derivative of y=(x+5)^{1/x} ?

The first derivative of y=(x+5)^{1/x} is (-(ln(x+5))/(x^2)+1/(x(x+5)))(x+5)^{1/x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = (x + 5)^{\frac{1}{x}}

(- \frac{ln ( x + 5 )}{x ^{2}} + \frac{1}{x ( x + 5 )}) (x + 5)^{\frac{1}{x}}

Solution steps

\frac{d}{d x} ((x + 5)^{\frac{1}{x}})

Apply exponent rule:

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

(x + 5)^{\frac{1}{x}} = e^{\frac{1}{x} l n (x + 5)}

= \frac{d}{d x} (e^{\frac{1}{x} l n (x + 5)})

Apply the chain rule:

e^{\frac{1}{x} l n (x + 5)} \frac{d}{d x} (\frac{1}{x} ln (x + 5))

= e^{\frac{1}{x} l n (x + 5)} \frac{d}{d x} (\frac{1}{x} ln (x + 5))

\frac{d}{d x} (\frac{1}{x} ln (x + 5)) = - \frac{ln ( x + 5 )}{x ^{2}} + \frac{1}{x ( x + 5 )}

= e^{\frac{1}{x} l n (x + 5)} (- \frac{ln ( x + 5 )}{x ^{2}} + \frac{1}{x ( x + 5 )})

e^{\frac{1}{x} l n (x + 5)} = (x + 5)^{\frac{1}{x}}

= (- \frac{ln ( x + 5 )}{x ^{2}} + \frac{1}{x ( x + 5 )}) (x + 5)^{\frac{1}{x}}

\int x^{2} (x^{3} + 5)^{9} d x

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{3} - x})

\int \frac{3 - 6 x}{25 - 9 x ^{2}} d x

\frac{\partial}{\partial x} ((x + y) e^{3 x - 4 y})

\frac{d ^{2}}{d x ^{2}} (\frac{e ^{x}}{8 x + 1})

What is the derivative of y=(x+5)^{1/x} ?
The derivative of y=(x+5)^{1/x} is (-(ln(x+5))/(x^2)+1/(x(x+5)))(x+5)^{1/x}
What is the first derivative of y=(x+5)^{1/x} ?
The first derivative of y=(x+5)^{1/x} is (-(ln(x+5))/(x^2)+1/(x(x+5)))(x+5)^{1/x}