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)

y = 3 x^{2} + 12 x + 6

y^{^{''}} + 4 y^{^{'}} + 4 y = 8 x^{2}

\frac{d}{d x} (x e^{x} y)

\frac{d ^{3}}{d x ^{3}} (cos (x) - sin (x))

\int \frac{6}{x ( x + 2 )} d x

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)