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Popular >

derivative of (e^x)/(x^2+3)

Solution

derivative of

\frac{e ^{x}}{x ^{2} + 3}

Solution

\frac{e ^{x} ( x ^{2} + 3 ) - 2 x e ^{x}}{( x ^{2} + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{x ^{2} + 3})

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} + 3 ) - \frac{d}{d x} ( x ^{2} + 3 ) e ^{x}}{( x ^{2} + 3 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 3) = 2 x

= \frac{e ^{x} ( x ^{2} + 3 ) - 2 x e ^{x}}{( x ^{2} + 3 ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of (e^x)/(x^2+3) ?
The derivative of (e^x)/(x^2+3) is (e^x(x^2+3)-2xe^x)/((x^2+3)^2)
What is the first derivative of (e^x)/(x^2+3) ?
The first derivative of (e^x)/(x^2+3) is (e^x(x^2+3)-2xe^x)/((x^2+3)^2)