What is the (x^{sqrt(x)})^' ?

The (x^{sqrt(x)})^' is x^{sqrt(x)}((ln(x))/(2sqrt(x))+1/(sqrt(x)))

What is the first (x^{sqrt(x)})^' ?

The first (x^{sqrt(x)})^' is x^{sqrt(x)}((ln(x))/(2sqrt(x))+1/(sqrt(x)))

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(x^{x})^{^{'}}

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

Solution steps

(x^{x})^{'}

Apply exponent rule:

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

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

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

Apply the chain rule:

e^{x l n (x)} (x ln (x))^{'}

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

60 e^{- 0}

6.2 \cdot 1 0^{- 3}

(8 x^{2}) \cdot (15 x^{3}) \cdot (4 x^{3})

\frac{e ^{40}}{e ^{38}}

What is the (x^{sqrt(x)})^' ?
The (x^{sqrt(x)})^' is x^{sqrt(x)}((ln(x))/(2sqrt(x))+1/(sqrt(x)))
What is the first (x^{sqrt(x)})^' ?
The first (x^{sqrt(x)})^' is x^{sqrt(x)}((ln(x))/(2sqrt(x))+1/(sqrt(x)))