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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

9 x^{2} - x^{3}

\int x 4 x - x^{2} d x

\frac{d}{d x} (\frac{2 e ^{l n^{2} (x)} ln ( x )}{x})

y^{^{''}} - 6 y^{^{'}} + 3 y = 0

x \to 3 lim (\frac{x ^{2} - 9}{x - 3})

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