What is the derivative of (e^{3x}/(x^{12)}) ?

The derivative of (e^{3x}/(x^{12)}) is (3e^{3x}(x-4))/(x^{13)}

What is the first derivative of (e^{3x}/(x^{12)}) ?

The first derivative of (e^{3x}/(x^{12)}) is (3e^{3x}(x-4))/(x^{13)}

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\frac{d}{d x} (\frac{e ^{3 x}}{x ^{12}})

\frac{3 e ^{3 x} ( x - 4 )}{x ^{13}}

Solution steps

\frac{d}{d x} (\frac{e ^{3 x}}{x ^{12}})

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 ^{12} - \frac{d}{d x} ( x ^{12} ) e ^{3 x}}{( x ^{12} ) ^{2}}

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

\frac{d}{d x} (x^{12}) = 12 x^{11}

= \frac{e ^{3 x} \cdot 3 x ^{12} - 12 x ^{11} e ^{3 x}}{( x ^{12} ) ^{2}}

Simplify

\frac{e ^{3 x} \cdot 3 x ^{12} - 12 x ^{11} e ^{3 x}}{( x ^{12} ) ^{2}} : \frac{3 e ^{3 x} ( x - 4 )}{x ^{13}}

= \frac{3 e ^{3 x} ( x - 4 )}{x ^{13}}

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

x \to 0.1 lim (\frac{5 sin ( x )}{x})

x \to 6 lim (\frac{x ^{2} - 3 x - 18}{x - 6})

(- 3.2) (6.3)

\int_{\frac{π}{4}}^{π} sin (2 x) d x

What is the derivative of (e^{3x}/(x^{12)}) ?
The derivative of (e^{3x}/(x^{12)}) is (3e^{3x}(x-4))/(x^{13)}
What is the first derivative of (e^{3x}/(x^{12)}) ?
The first derivative of (e^{3x}/(x^{12)}) is (3e^{3x}(x-4))/(x^{13)}