What is the derivative of (1+2/x ^x) ?

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

What is the first derivative of (1+2/x ^x) ?

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

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

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

Solution steps

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

Apply exponent rule:

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

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

= \frac{d}{d x} (e^{x l n (1 + \frac{2}{x})})

Apply the chain rule:

e^{x l n (1 + \frac{2}{x})} \frac{d}{d x} (x ln (1 + \frac{2}{x}))

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

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

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

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

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

\frac{d}{d x} (\frac{e ^{3 x}}{e ^{3 x} + 2})

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

\int (\frac{1}{x ^{3}}) d x

\int x^{n + 1} d x

\int x sin (\frac{1}{5} x) d x

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