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Popular >

derivative of x^{sqrt(x)}

Solution

derivative of

x^{x}

Solution

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})

Popular Examples

tangent of f(x)=((e^x))/x ,\at x=1 tangent of

f (x) = \frac{( e ^{x} )}{x}, at x = 1

laplacetransform (t^3e^{-,\at})laplace transform

(t^{3} e^{-, at})

limit as x approaches 3-of (|3+x|)/(3-x)

x \to 3 - lim (\frac{∣ 3 + x ∣}{3 - x})

(\partial)/(\partial y)(e^ysin(xy))

\frac{\partial}{\partial y} (e^{y} sin (x y))

integral of (9x)/((2-x^2)^3)

\int \frac{9 x}{( 2 - x ^{2} ) ^{3}} d x

Frequently Asked Questions (FAQ)

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