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

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

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

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

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

\frac{4 e ^{4 x} x - e ^{4 x}}{x ^{2}}

Solution steps

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

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 - \frac{d x}{d x} e ^{4 x}}{x ^{2}}

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

\frac{d x}{d x} = 1

= \frac{e ^{4 x} \cdot 4 x - 1 \cdot e ^{4 x}}{x ^{2}}

Simplify

= \frac{4 e ^{4 x} x - e ^{4 x}}{x ^{2}}

\frac{d}{d t} (e^{a t})

\frac{6 x + 4 x ^{2}}{( 3 + 4 x ) ^{2}}

y^{^{''}} - y = 1

\frac{d y}{d x} = \frac{8 y ^{2}}{x}

\int 5 e^{- 0.2 x} d x

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