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

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

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

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

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derivative of

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

\frac{- e ^{x} - 2}{e ^{2 x}}

Solution steps

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

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

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

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

Simplify

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

= \frac{- e ^{x} - 2}{e ^{2 x}}

\frac{( e ^{2 x} - 1 )}{x}, - 0.5

\frac{d y}{d x} = (\frac{sec ( x )}{y})^{2}

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

(2 x y^{- 1}) d x + (2 - 4 x^{2} y^{- 2}) d y = 0

y = 2 ln (x), at x = 4

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