What is (\partial)/(\partial x)(e^{-x^3}) ?

The answer to (\partial)/(\partial x)(e^{-x^3}) is -3e^{-x^3}x^2

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(\partial)/(\partial x)(e^{-x^3})

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

- 3 e^{- x^{3}} x^{2}

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- x^{3}) = - 3 x^{2}

= e^{- x^{3}} (- 3 x^{2})

Simplify

= - 3 e^{- x^{3}} x^{2}

f (x) = \frac{3}{x}

\frac{\partial}{\partial y} (6 x^{\frac{1}{3}} y^{\frac{2}{3}})

\frac{\partial}{\partial x} (\frac{4 x}{( y + 2 z ) ^{3}})

x \to 0 lim (\frac{1}{x} sin (x))

\int_{0}^{3 π} ∣ sin (x) ∣ d x

What is (\partial)/(\partial x)(e^{-x^3}) ?
The answer to (\partial)/(\partial x)(e^{-x^3}) is -3e^{-x^3}x^2