What is the derivative of (e^x/(5x^2+1)) ?

The derivative of (e^x/(5x^2+1)) is (e^x(5x^2+1)-10xe^x)/((5x^2+1)^2)

What is the first derivative of (e^x/(5x^2+1)) ?

The first derivative of (e^x/(5x^2+1)) is (e^x(5x^2+1)-10xe^x)/((5x^2+1)^2)

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\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2} + 1})

\frac{e ^{x} ( 5 x ^{2} + 1 ) - 10 x e ^{x}}{( 5 x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{5 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} ) ( 5 x ^{2} + 1 ) - \frac{d}{d x} ( 5 x ^{2} + 1 ) e ^{x}}{( 5 x ^{2} + 1 ) ^{2}}

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

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

= \frac{e ^{x} ( 5 x ^{2} + 1 ) - 10 x e ^{x}}{( 5 x ^{2} + 1 ) ^{2}}

\int π sin (\frac{n x}{2}) d x

\frac{d}{d x} (6 x^{3} - 9 x + 4)

x \to - 1 lim (4)

\frac{\partial}{\partial x} (f (y, x) (\frac{y}{x}))

n = 1 \sum \infty \frac{( - 1 ) ^{6 n}}{n}

What is the derivative of (e^x/(5x^2+1)) ?
The derivative of (e^x/(5x^2+1)) is (e^x(5x^2+1)-10xe^x)/((5x^2+1)^2)
What is the first derivative of (e^x/(5x^2+1)) ?
The first derivative of (e^x/(5x^2+1)) is (e^x(5x^2+1)-10xe^x)/((5x^2+1)^2)