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

The derivative of x^{1/(x^2}) is x^{(1-3x^2)/(x^2)}(-2ln(x)+1)

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

The first derivative of x^{1/(x^2}) is x^{(1-3x^2)/(x^2)}(-2ln(x)+1)

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

= e^{\frac{1}{x ^{2}} l n (x)} \frac{- 2 ln ( x ) + 1}{x ^{3}}

Simplify

e^{\frac{1}{x ^{2}} l n (x)} \frac{- 2 ln ( x ) + 1}{x ^{3}} : x^{\frac{1 - 3 x ^{2}}{x ^{2}}} (- 2 ln (x) + 1)

= x^{\frac{1 - 3 x ^{2}}{x ^{2}}} (- 2 ln (x) + 1)

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

\int_{2}^{4} (2 + u)^{2} d u

\frac{d}{d x} (- ln (x) cos (x))

\int (5 cos (3 x) - 4 sin (5 x)) d x

n = 5 \sum \infty \frac{5 ^{n}}{1 2 ^{n}}

What is the derivative of x^{1/(x^2}) ?
The derivative of x^{1/(x^2}) is x^{(1-3x^2)/(x^2)}(-2ln(x)+1)
What is the first derivative of x^{1/(x^2}) ?
The first derivative of x^{1/(x^2}) is x^{(1-3x^2)/(x^2)}(-2ln(x)+1)