What is the derivative of x^{x^2} ?

The derivative of x^{x^2} is x^{x^2}(2xln(x)+x)

What is the first derivative of x^{x^2} ?

The first derivative of x^{x^2} is x^{x^2}(2xln(x)+x)

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derivative of

x^{x^{2}}

x^{x^{2}} (2 x ln (x) + x)

Solution steps

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

Apply exponent rule:

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

x^{x^{2}} = e^{x^{2} l n (x)}

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

Apply the chain rule:

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

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

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

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

e^{x^{2} l n (x)} = x^{x^{2}}

= x^{x^{2}} (2 x ln (x) + x)

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

\int (x^{2} - 3 x + 6) d x

\int 2 x cos^{2} (x) d x

\frac{d}{d x} (x^{2} - 3 x - 4)

x \to 0 + lim (e^{\frac{2}{x}})

What is the derivative of x^{x^2} ?
The derivative of x^{x^2} is x^{x^2}(2xln(x)+x)
What is the first derivative of x^{x^2} ?
The first derivative of x^{x^2} is x^{x^2}(2xln(x)+x)