What is the derivative of (e^{4x}/(x^{12)}) ?

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

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

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

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\frac{d}{d x} (\frac{e ^{4 x}}{x ^{12}})

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

Solution steps

\frac{d}{d x} (\frac{e ^{4 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 ^{4 x} ) x ^{12} - \frac{d}{d x} ( x ^{12} ) e ^{4 x}}{( x ^{12} ) ^{2}}

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

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

= \frac{e ^{4 x} \cdot 4 x ^{12} - 12 x ^{11} e ^{4 x}}{( x ^{12} ) ^{2}}

Simplify

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

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

f (x) = 4 x^{5} - x^{3} - 2

x \to + 0 - lim (\frac{e ^{x}}{x ^{3}})

n \to \infty lim (5^{n})

\frac{\partial}{\partial y} (x^{2} - x y + y^{2})

\int \frac{x}{( x + 2 ) ( x - 4 )} d x

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