What is the derivative of x^{2/x} ?

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

What is the first derivative of x^{2/x} ?

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

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derivative of

x^{\frac{2}{x}}

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 lim (\frac{5 x + x ^{2}}{x})

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

\int x ln^{4} (x) d x

\frac{\partial}{\partial x} (\frac{t}{c ^{2} t ^{2} - x ^{2}})

f (x) = \frac{12}{x + 7}

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