What is the derivative of-(e^{-2x^3}/(4x^4)) ?

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

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

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

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

\frac{e ^{- 2 x^{3}} ( 3 x ^{3} + 2 )}{2 x ^{5}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (e^{- 2 x^{3}}) = - 6 e^{- 2 x^{3}} x^{2}

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

= - \frac{1}{4} \cdot \frac{( - 6 e ^{- 2 x^{3}} x ^{2} ) x ^{4} - 4 x ^{3} e ^{- 2 x^{3}}}{( x ^{4} ) ^{2}}

Simplify

- \frac{1}{4} \cdot \frac{( - 6 e ^{- 2 x^{3}} x ^{2} ) x ^{4} - 4 x ^{3} e ^{- 2 x^{3}}}{( x ^{4} ) ^{2}} : \frac{e ^{- 2 x^{3}} ( 3 x ^{3} + 2 )}{2 x ^{5}}

= \frac{e ^{- 2 x^{3}} ( 3 x ^{3} + 2 )}{2 x ^{5}}

x \to - 4 lim ([x])

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

\int \frac{3}{z} d z

\int arctan (x^{2}) d x

x \to - 5 + lim (\frac{- 3}{x ^{2} - 25})

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