What is the derivative of (x^3/(e^{2x)}) ?

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

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

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

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\frac{d}{d x} (\frac{x ^{3}}{e ^{2 x}})

\frac{x ^{2} ( 3 - 2 x )}{e ^{2 x}}

Solution steps

\frac{d}{d x} (\frac{x ^{3}}{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 ^{3} ) e ^{2 x} - \frac{d}{d x} ( e ^{2 x} ) x ^{3}}{( e ^{2 x} ) ^{2}}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= \frac{3 x ^{2} e ^{2 x} - e ^{2 x} \cdot 2 x ^{3}}{( e ^{2 x} ) ^{2}}

Simplify

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

= \frac{x ^{2} ( 3 - 2 x )}{e ^{2 x}}

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