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

The derivative of (e^x)/((1+2x)) is (2e^xx-e^x)/((1+2x)^2)

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

The first derivative of (e^x)/((1+2x)) is (2e^xx-e^x)/((1+2x)^2)

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

e^{x} (1 + 2 x) - 2 e^{x} : 2 e^{x} x - e^{x}

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

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

x (60 - x)^{3}

y^{1} - n

(1 + x)^{x}

\frac{3}{cos ( x )}

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