What is the derivative of x^2e^{-x^3} ?

The derivative of x^2e^{-x^3} is 2e^{-x^3}x-3e^{-x^3}x^4

What is the first derivative of x^2e^{-x^3} ?

The first derivative of x^2e^{-x^3} is 2e^{-x^3}x-3e^{-x^3}x^4

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

2 e^{- x^{3}} x - 3 e^{- x^{3}} x^{4}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = e^{- x^{3}}

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

Simplify

2 x e^{- x^{3}} + (- 3 e^{- x^{3}} x^{2}) x^{2} : 2 e^{- x^{3}} x - 3 e^{- x^{3}} x^{4}

= 2 e^{- x^{3}} x - 3 e^{- x^{3}} x^{4}

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

\frac{d}{d x} (3 x^{2} - 10 x + 7)

\int_{0}^{1} (1 + x)^{8} d x

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

\frac{d}{d x} (\frac{3 x + 1}{x ^{2} + 1})

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