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

The derivative of (e^{x+1}/(x^2+1)) is (e^{x+1}(x^2+1)-2xe^{x+1})/((x^2+1)^2)

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

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

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

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

Solution steps

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

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

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

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

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