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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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