What is (sqrt(x^2+a^2))^{e^{x^2}} ?

The solution to (sqrt(x^2+a^2))^{e^{x^2}} is (x^2+a^2)^{(e^{x^2})/2}

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simplify (sqrt(x^2+a^2))^{e^{x^2}}

simplify

(x^{2} + a^{2})^{e^{x^{2}}}

(x^{2} + a^{2})^{\frac{e ^{x^{2}}}{2}}

Solution steps

(x^{2} + a^{2})^{e^{x^{2}}}

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

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

Simplify

\frac{1}{2} e^{x^{2}} : \frac{e ^{x^{2}}}{2}

= (x^{2} + a^{2})^{\frac{e ^{x^{2}}}{2}}

\frac{d}{d x} (2 a - b x)

x \to 6 - lim (\frac{x}{6 - x})

\int x^{2} + x + 1 d x

\frac{\partial}{\partial x} ((y + x)^{2})

\frac{\partial}{\partial x} (sin (x - y))

What is (sqrt(x^2+a^2))^{e^{x^2}} ?
The solution to (sqrt(x^2+a^2))^{e^{x^2}} is (x^2+a^2)^{(e^{x^2})/2}