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Popular >

derivative of (e^x)/(x^2+14)

Solution

derivative of

\frac{e ^{x}}{x ^{2} + 14}

Solution

\frac{e ^{x} ( x ^{2} + 14 ) - 2 x e ^{x}}{( x ^{2} + 14 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{x ^{2} + 14})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( x ^{2} + 14 ) - \frac{d}{d x} ( x ^{2} + 14 ) e ^{x}}{( x ^{2} + 14 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 14) = 2 x

= \frac{e ^{x} ( x ^{2} + 14 ) - 2 x e ^{x}}{( x ^{2} + 14 ) ^{2}}

Popular Examples

integral from 1 to 2 of 7/(x^3+4x)

\int_{1}^{2} \frac{7}{x ^{3} + 4 x} d x

(\partial)/(\partial y)(sin(y)-ysin(x))

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

derivative of e^{xsqrt(x^2+1)}

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

limit as t approaches 1-of (2t)/(t^2-1)

t \to 1 - lim (\frac{2 t}{t ^{2} - 1})

y^{^{''}} - 2 y + 4 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of (e^x)/(x^2+14) ?
The derivative of (e^x)/(x^2+14) is (e^x(x^2+14)-2xe^x)/((x^2+14)^2)
What is the first derivative of (e^x)/(x^2+14) ?
The first derivative of (e^x)/(x^2+14) is (e^x(x^2+14)-2xe^x)/((x^2+14)^2)