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Popular >

derivative of (e^x/(2x^2+1))

Solution

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

Solution

\frac{e ^{x} ( 2 x ^{2} + 1 ) - 4 x e ^{x}}{( 2 x ^{2} + 1 ) ^{2}}

Solution steps

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

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

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

= \frac{e ^{x} ( 2 x ^{2} + 1 ) - 4 x e ^{x}}{( 2 x ^{2} + 1 ) ^{2}}

Popular Examples

(dy)/(dx)+x^2y=10x^2,y(1)=5

\frac{d y}{d x} + x^{2} y = 10 x^{2}, y (1) = 5

integral from-infinity to 0 of 1/(5-2x)

\int_{- \infty}^{0} \frac{1}{5 - 2 x} d x

derivative of (3x)/(7x^2+1)derivative of

\frac{3 x}{7 x ^{2} + 1}

sum from n=1 to infinity of 5/(6n+4)

n = 1 \sum \infty \frac{5}{6 n + 4}

(\partial)/(\partial x)(sqrt(16-x^2))

\frac{\partial}{\partial x} (16 - x^{2})

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/(2x^2+1)) ?
The derivative of (e^x/(2x^2+1)) is (e^x(2x^2+1)-4xe^x)/((2x^2+1)^2)
What is the first derivative of (e^x/(2x^2+1)) ?
The first derivative of (e^x/(2x^2+1)) is (e^x(2x^2+1)-4xe^x)/((2x^2+1)^2)