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

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

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

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

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derivative of

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

= - 4 \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}}

= - 4 \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}

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

Simplify

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

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

x \to 0 lim (+ (e^{- \frac{1}{x}}))

\int 2 x \cdot e^{x^{2}} d x

\int_{x}^{\frac{1}{2}} 8 d y

(2 x - 1) d x + (7 y + 3) d y = 0

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

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