What is the derivative of (e^{2x}/(x^4)) ?

The derivative of (e^{2x}/(x^4)) is (2e^{2x}(x-2))/(x^5)

What is the first derivative of (e^{2x}/(x^4)) ?

The first derivative of (e^{2x}/(x^4)) is (2e^{2x}(x-2))/(x^5)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{e ^{2 x} \cdot 2 x ^{4} - 4 x ^{3} e ^{2 x}}{( x ^{4} ) ^{2}}

Simplify

\frac{e ^{2 x} \cdot 2 x ^{4} - 4 x ^{3} e ^{2 x}}{( x ^{4} ) ^{2}} : \frac{2 e ^{2 x} ( x - 2 )}{x ^{5}}

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

g (f) = f^{8}

\int \frac{1}{x + 5} d x

e^{- 3 t} + 3

\int \frac{- t}{( t + 1 ) - ( t + 1 )} d t

\frac{\partial}{\partial t} (\frac{3 y ^{2} - t ^{2}}{y ^{5}})

What is the derivative of (e^{2x}/(x^4)) ?
The derivative of (e^{2x}/(x^4)) is (2e^{2x}(x-2))/(x^5)
What is the first derivative of (e^{2x}/(x^4)) ?
The first derivative of (e^{2x}/(x^4)) is (2e^{2x}(x-2))/(x^5)