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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derivative of

\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}}

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{9}})

y^{^{'}} = \frac{( ( y - y ^{2} ) t )}{1 + t ^{2}}, y (0) = \frac{1}{2}

\int 2 t^{\frac{3}{2}} d t

\int \frac{9}{( x - 7 ) ( x + 2 )} d x

\frac{d x}{d t} = x b

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)