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

The derivative of (e^{2x}/(x^3)) is (e^{2x}(2x-3))/(x^4)

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

The first derivative of (e^{2x}/(x^3)) is (e^{2x}(2x-3))/(x^4)

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

\frac{e ^{2 x} ( 2 x - 3 )}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{e ^{2 x} \cdot 2 x ^{3} - 3 x ^{2} e ^{2 x}}{( x ^{3} ) ^{2}} : \frac{e ^{2 x} ( 2 x - 3 )}{x ^{4}}

= \frac{e ^{2 x} ( 2 x - 3 )}{x ^{4}}

What is the derivative of (e^{2x}/(x^3)) ?
The derivative of (e^{2x}/(x^3)) is (e^{2x}(2x-3))/(x^4)
What is the first derivative of (e^{2x}/(x^3)) ?
The first derivative of (e^{2x}/(x^3)) is (e^{2x}(2x-3))/(x^4)