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Popular >

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

Solution

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

Solution

\frac{e ^{\frac{x ^{2}}{4}} x}{2}

Solution steps

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

Simplify

e^{(\frac{x}{2})^{2}} : e^{\frac{x ^{2}}{4}}

= \frac{d}{d x} (e^{\frac{x ^{2}}{4}})

Apply the chain rule:

e^{\frac{x ^{2}}{4}} \frac{d}{d x} (\frac{x ^{2}}{4})

= e^{\frac{x ^{2}}{4}} \frac{d}{d x} (\frac{x ^{2}}{4})

\frac{d}{d x} (\frac{x ^{2}}{4}) = \frac{x}{2}

= e^{\frac{x ^{2}}{4}} \frac{x}{2}

Multiply fractions:

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

= \frac{e ^{\frac{x ^{2}}{4}} x}{2}

Popular Examples

derivative of ((2x^2)/(x-2))

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

slope of f(x)=x^2-5 slope

f (x) = x^{2} - 5

derivative of 3cos(x-4sin(x))

\frac{d}{d x} (3 cos (x) - 4 sin (x))

derivative of (e^x)/(7x^2+5)derivative of

\frac{e ^{x}}{7 x ^{2} + 5}

limit as x approaches 9 of x^2

x \to 9 lim (x^{2})

Frequently Asked Questions (FAQ)

What is the derivative of e^{(x/2 ^2}) ?
The derivative of e^{(x/2 ^2}) is (e^{(x^2)/4}x)/(2)
What is the first derivative of e^{(x/2 ^2}) ?
The first derivative of e^{(x/2 ^2}) is (e^{(x^2)/4}x)/(2)