What is the derivative of (e^{3x}/(x^6)) ?

The derivative of (e^{3x}/(x^6)) is (3e^{3x}(x-2))/(x^7)

What is the first derivative of (e^{3x}/(x^6)) ?

The first derivative of (e^{3x}/(x^6)) is (3e^{3x}(x-2))/(x^7)

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\frac{d}{d x} (\frac{e ^{3 x}}{x ^{6}})

\frac{3 e ^{3 x} ( x - 2 )}{x ^{7}}

Solution steps

\frac{d}{d x} (\frac{e ^{3 x}}{x ^{6}})

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 ^{6} - \frac{d}{d x} ( x ^{6} ) e ^{3 x}}{( x ^{6} ) ^{2}}

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

\frac{d}{d x} (x^{6}) = 6 x^{5}

= \frac{e ^{3 x} \cdot 3 x ^{6} - 6 x ^{5} e ^{3 x}}{( x ^{6} ) ^{2}}

Simplify

\frac{e ^{3 x} \cdot 3 x ^{6} - 6 x ^{5} e ^{3 x}}{( x ^{6} ) ^{2}} : \frac{3 e ^{3 x} ( x - 2 )}{x ^{7}}

= \frac{3 e ^{3 x} ( x - 2 )}{x ^{7}}

What is the derivative of (e^{3x}/(x^6)) ?
The derivative of (e^{3x}/(x^6)) is (3e^{3x}(x-2))/(x^7)
What is the first derivative of (e^{3x}/(x^6)) ?
The first derivative of (e^{3x}/(x^6)) is (3e^{3x}(x-2))/(x^7)