What is the derivative of (e^{4x}/(x^8)) ?

The derivative of (e^{4x}/(x^8)) is (4e^{4x}(x-2))/(x^9)

What is the first derivative of (e^{4x}/(x^8)) ?

The first derivative of (e^{4x}/(x^8)) is (4e^{4x}(x-2))/(x^9)

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\frac{d}{d x} (\frac{e ^{4 x}}{x ^{8}})

\frac{4 e ^{4 x} ( x - 2 )}{x ^{9}}

Solution steps

\frac{d}{d x} (\frac{e ^{4 x}}{x ^{8}})

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 ^{8} - \frac{d}{d x} ( x ^{8} ) e ^{4 x}}{( x ^{8} ) ^{2}}

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

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{e ^{4 x} \cdot 4 x ^{8} - 8 x ^{7} e ^{4 x}}{( x ^{8} ) ^{2}}

Simplify

\frac{e ^{4 x} \cdot 4 x ^{8} - 8 x ^{7} e ^{4 x}}{( x ^{8} ) ^{2}} : \frac{4 e ^{4 x} ( x - 2 )}{x ^{9}}

= \frac{4 e ^{4 x} ( x - 2 )}{x ^{9}}

\int cos^{2} (t) sin (t) d t

n = 3 \sum \infty (\frac{4}{5})^{n}

\frac{d y}{d x} = y^{2} + 1, y (1) = 0

y^{^{''}} + 2 y^{^{'}} = 0

\frac{d y}{d x} = e^{2 y + 9 x}

What is the derivative of (e^{4x}/(x^8)) ?
The derivative of (e^{4x}/(x^8)) is (4e^{4x}(x-2))/(x^9)
What is the first derivative of (e^{4x}/(x^8)) ?
The first derivative of (e^{4x}/(x^8)) is (4e^{4x}(x-2))/(x^9)