What is the derivative of (e^{5x}/(x^{15)}) ?

The derivative of (e^{5x}/(x^{15)}) is (5e^{5x}(x-3))/(x^{16)}

What is the first derivative of (e^{5x}/(x^{15)}) ?

The first derivative of (e^{5x}/(x^{15)}) is (5e^{5x}(x-3))/(x^{16)}

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\frac{d}{d x} (\frac{e ^{5 x}}{x ^{15}})

\frac{5 e ^{5 x} ( x - 3 )}{x ^{16}}

Solution steps

\frac{d}{d x} (\frac{e ^{5 x}}{x ^{15}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{5 x} ) x ^{15} - \frac{d}{d x} ( x ^{15} ) e ^{5 x}}{( x ^{15} ) ^{2}}

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

\frac{d}{d x} (x^{15}) = 15 x^{14}

= \frac{e ^{5 x} \cdot 5 x ^{15} - 15 x ^{14} e ^{5 x}}{( x ^{15} ) ^{2}}

Simplify

\frac{e ^{5 x} \cdot 5 x ^{15} - 15 x ^{14} e ^{5 x}}{( x ^{15} ) ^{2}} : \frac{5 e ^{5 x} ( x - 3 )}{x ^{16}}

= \frac{5 e ^{5 x} ( x - 3 )}{x ^{16}}

What is the derivative of (e^{5x}/(x^{15)}) ?
The derivative of (e^{5x}/(x^{15)}) is (5e^{5x}(x-3))/(x^{16)}
What is the first derivative of (e^{5x}/(x^{15)}) ?
The first derivative of (e^{5x}/(x^{15)}) is (5e^{5x}(x-3))/(x^{16)}