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

The derivative of (e^x/(4x^2+1)) is (e^x(4x^2+1)-8xe^x)/((4x^2+1)^2)

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

The first derivative of (e^x/(4x^2+1)) is (e^x(4x^2+1)-8xe^x)/((4x^2+1)^2)

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

\frac{e ^{x} ( 4 x ^{2} + 1 ) - 8 x e ^{x}}{( 4 x ^{2} + 1 ) ^{2}}

Solution steps

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

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

\frac{d}{d x} (4 x^{2} + 1) = 8 x

= \frac{e ^{x} ( 4 x ^{2} + 1 ) - 8 x e ^{x}}{( 4 x ^{2} + 1 ) ^{2}}

\int e^{x} cos (4 y) d x

x \to 1 lim (ln (x - 1))

\int \frac{( x + 1 ) ^{2}}{x ^{3} + x} d x

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

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

What is the derivative of (e^x/(4x^2+1)) ?
The derivative of (e^x/(4x^2+1)) is (e^x(4x^2+1)-8xe^x)/((4x^2+1)^2)
What is the first derivative of (e^x/(4x^2+1)) ?
The first derivative of (e^x/(4x^2+1)) is (e^x(4x^2+1)-8xe^x)/((4x^2+1)^2)