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

The derivative of (1-x/(e^{2x)}) is -(-2x+3)/(e^{2x)}

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

The first derivative of (1-x/(e^{2x)}) is -(-2x+3)/(e^{2x)}

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

- \frac{- 2 x + 3}{e ^{2 x}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (1 - x) = - 1

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

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

Simplify

\frac{( - 1 ) e ^{2 x} - e ^{2 x} \cdot 2 ( 1 - x )}{( e ^{2 x} ) ^{2}} : - \frac{- 2 x + 3}{e ^{2 x}}

= - \frac{- 2 x + 3}{e ^{2 x}}

\int_{0}^{2 π} 9 x^{2} sin (\frac{1}{4} x) d x

\int sin (3) (x) cos (x) d x

x \to π lim (\frac{x}{sin ( x )})

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

y = 5 e^{x} cos (x), (0, 5)

What is the derivative of (1-x/(e^{2x)}) ?
The derivative of (1-x/(e^{2x)}) is -(-2x+3)/(e^{2x)}
What is the first derivative of (1-x/(e^{2x)}) ?
The first derivative of (1-x/(e^{2x)}) is -(-2x+3)/(e^{2x)}