What is the derivative of (e^{8x}/(3x^4)) ?

The derivative of (e^{8x}/(3x^4)) is (4e^{8x}(2x-1))/(3x^5)

What is the first derivative of (e^{8x}/(3x^4)) ?

The first derivative of (e^{8x}/(3x^4)) is (4e^{8x}(2x-1))/(3x^5)

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\frac{d}{d x} (\frac{e ^{8 x}}{3 x ^{4}})

\frac{4 e ^{8 x} ( 2 x - 1 )}{3 x ^{5}}

Solution steps

\frac{d}{d x} (\frac{e ^{8 x}}{3 x ^{4}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{3} \frac{d}{d x} (\frac{e ^{8 x}}{x ^{4}})

Apply the Quotient Rule:

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

= \frac{1}{3} \cdot \frac{\frac{d}{d x} ( e ^{8 x} ) x ^{4} - \frac{d}{d x} ( x ^{4} ) e ^{8 x}}{( x ^{4} ) ^{2}}

\frac{d}{d x} (e^{8 x}) = e^{8 x} \cdot 8

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

= \frac{1}{3} \cdot \frac{e ^{8 x} \cdot 8 x ^{4} - 4 x ^{3} e ^{8 x}}{( x ^{4} ) ^{2}}

Simplify

\frac{1}{3} \cdot \frac{e ^{8 x} \cdot 8 x ^{4} - 4 x ^{3} e ^{8 x}}{( x ^{4} ) ^{2}} : \frac{4 e ^{8 x} ( 2 x - 1 )}{3 x ^{5}}

= \frac{4 e ^{8 x} ( 2 x - 1 )}{3 x ^{5}}

\int (3 x - 6 x) d x

x \to 0 lim (\frac{2 x ^{2} - x}{x})

y = (x)^{x}

f (x) = 7 sin (x)

\frac{d}{d x} (\frac{- 2}{x})

What is the derivative of (e^{8x}/(3x^4)) ?
The derivative of (e^{8x}/(3x^4)) is (4e^{8x}(2x-1))/(3x^5)
What is the first derivative of (e^{8x}/(3x^4)) ?
The first derivative of (e^{8x}/(3x^4)) is (4e^{8x}(2x-1))/(3x^5)