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

The derivative of ((e^x))/(3x^4) is (e^x(x-4))/(3x^5)

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

The first derivative of ((e^x))/(3x^4) is (e^x(x-4))/(3x^5)

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

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

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

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

Simplify

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

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

\int tan^{5} (5 x) (sec^{3} (5 x) - 1) d x

\frac{\partial}{\partial x} (y \cdot ln (x^{4} + y^{4} + 1) - 8)

x \to 0 lim (\frac{( 343 + x ) ^{\frac{1}{3}} - 7}{( x )})

\int \frac{5 x + 2}{( x - 5 ) ( x + 5 ) ( x - 1 )} d x

\frac{d}{d x} (\frac{x y ^{3}}{x ^{2} + y ^{2}})

What is the derivative of ((e^x))/(3x^4) ?
The derivative of ((e^x))/(3x^4) is (e^x(x-4))/(3x^5)
What is the first derivative of ((e^x))/(3x^4) ?
The first derivative of ((e^x))/(3x^4) is (e^x(x-4))/(3x^5)