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Popular >

derivative of e^{(x^2/(2a)})

Solution

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

Solution

\frac{e ^{\frac{x ^{2}}{2 a}} x}{a}

Solution steps

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

Apply the chain rule:

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

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

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

= e^{\frac{x ^{2}}{2 a}} \frac{x}{a}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{\frac{x ^{2}}{2 a}} x}{a}

Popular Examples

y^{^{'}} = y^{2} - 8

limit as x approaches 0 of (5/(1+x)-5)/x

x \to 0 lim (\frac{\frac{5}{1 + x} - 5}{x})

derivative of sin(2xdx)

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

(xysin(x)+2ycos(x))dx+(2xcos(x))dy=0

(x y sin (x) + 2 y cos (x)) d x + (2 x cos (x)) d y = 0

limit as h approaches 0 of ((2-h)^3-8)/h

h \to 0 lim (\frac{( 2 - h ) ^{3} - 8}{h})

Frequently Asked Questions (FAQ)

What is the derivative of e^{(x^2/(2a)}) ?
The derivative of e^{(x^2/(2a)}) is (e^{(x^2)/(2a)}x)/a
What is the first derivative of e^{(x^2/(2a)}) ?
The first derivative of e^{(x^2/(2a)}) is (e^{(x^2)/(2a)}x)/a