What is the derivative of e^{x/a} ?

The derivative of e^{x/a} is (e^{x/a})/a

What is the first derivative of e^{x/a} ?

The first derivative of e^{x/a} is (e^{x/a})/a

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

\frac{e ^{\frac{x}{a}}}{a}

Solution steps

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

Apply the chain rule:

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

= e^{\frac{x}{a}} \frac{d}{d x} (\frac{x}{a})

\frac{d}{d x} (\frac{x}{a}) = \frac{1}{a}

= e^{\frac{x}{a}} \frac{1}{a}

Simplify

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

= \frac{e ^{\frac{x}{a}}}{a}

\int x e^{- \frac{1}{2} x} d x

x \to 2 lim (1 0^{x^{2} - 4 x})

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

f (x) = 2 x 1 - x^{2}

f (x) = (8 x^{2} - 13 x) e^{x}

What is the derivative of e^{x/a} ?
The derivative of e^{x/a} is (e^{x/a})/a
What is the first derivative of e^{x/a} ?
The first derivative of e^{x/a} is (e^{x/a})/a