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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

= \frac{e ^{x^{2}} \cdot 2 xx - 1 \cdot e ^{x^{2}}}{x ^{2}}

e^{x^{2}} \cdot 2 xx - 1 \cdot e^{x^{2}} = 2 e^{x^{2}} x^{2} - e^{x^{2}}

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

Popular Examples

derivative of y= 2/(3sqrt(x^3))derivative of

y = \frac{2}{3 x ^{3}}

(dy)/(dt)=0.0572(400-y)

\frac{d y}{d t} = 0.0572 (400 - y)

integral of (3ln(x+7))/(x^2)

\int \frac{3 ln ( x + 7 )}{x ^{2}} d x

derivative of 1/(3x^2+4x)derivative of

\frac{1}{3 x ^{2} + 4 x}

(\partial)/(\partial x)((9xy^2)/(x^2+y^4))

\frac{\partial}{\partial x} (\frac{9 x y ^{2}}{x ^{2} + y ^{4}})

Frequently Asked Questions (FAQ)

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