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

The derivative of f(x)=4e^{x^{-3}} is -(12e^{1/(x^3)})/(x^4)

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

The first derivative of f(x)=4e^{x^{-3}} is -(12e^{1/(x^3)})/(x^4)

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derivative of

f (x) = 4 e^{x^{- 3}}

- \frac{12 e ^{\frac{1}{x ^{3}}}}{x ^{4}}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

4 e^{x^{- 3}} (- \frac{3}{x ^{4}}) : - \frac{12 e ^{\frac{1}{x ^{3}}}}{x ^{4}}

= - \frac{12 e ^{\frac{1}{x ^{3}}}}{x ^{4}}

What is the derivative of f(x)=4e^{x^{-3}} ?
The derivative of f(x)=4e^{x^{-3}} is -(12e^{1/(x^3)})/(x^4)
What is the first derivative of f(x)=4e^{x^{-3}} ?
The first derivative of f(x)=4e^{x^{-3}} is -(12e^{1/(x^3)})/(x^4)