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

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

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

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

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derivative of

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

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

Solution steps

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

Simplify

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

= \frac{d}{d x} ((\frac{2}{x})^{x})

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

2 x^{20}

\frac{d}{d x} (- 100 + 177.5 - 1.5 (x - 30))

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

(x + y)^{3}

\frac{2}{x ^{3}} + \frac{2}{x ^{3}} - 4 x

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