What is the derivative of y=x^{sqrt(x)} ?

The derivative of y=x^{sqrt(x)} is x^{sqrt(x)}((ln(x))/(2sqrt(x))+1/(sqrt(x)))

What is the first derivative of y=x^{sqrt(x)} ?

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

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derivative of

y = x^{x}

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

Solution steps

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

Apply exponent rule:

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

x^{x} = e^{x l n (x)}

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

Apply the chain rule:

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

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

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

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

e^{x l n (x)} = x^{x}

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

x \to + π + lim (csc (x))

\frac{d}{d x} ((x - 42)^{2} - 3 x ln ((x - 100)^{2}))

(e^{x} y) d y = (e^{- y} + e^{- 2 x - y}) d x

ln (t)

x \to 5 lim (2 x^{2} - 3 x + 4)

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