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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

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

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

\frac{d}{d x} (\frac{x}{2 - x ^{2}})

f (x) = \frac{x}{x - 2}, at x = 3

(- 5.2) (2.5)

\frac{d}{d x} (sin (x + x) + 5)

\frac{\partial}{\partial x} (6 + x ln (x y - 9))

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