What is the derivative of (e^{3x}/(x^{15)}) ?

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

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

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

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\frac{d}{d x} (\frac{e ^{3 x}}{x ^{15}})

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

Solution steps

\frac{d}{d x} (\frac{e ^{3 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 ^{3 x} ) x ^{15} - \frac{d}{d x} ( x ^{15} ) e ^{3 x}}{( x ^{15} ) ^{2}}

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

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

= \frac{e ^{3 x} \cdot 3 x ^{15} - 15 x ^{14} e ^{3 x}}{( x ^{15} ) ^{2}}

Simplify

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

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

\int \frac{ln ( 9 x )}{x} d x

\int (1 - x) (1 - 2 x) (1 - 3 x) d x

\int \frac{x ^{8}}{x ^{9} - 2} d x

\int_{0}^{5} x e^{- x} d x

\int cos (8)

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