What is the derivative of xe^{-x^{10}} ?

The derivative of xe^{-x^{10}} is e^{-x^{10}}-10e^{-x^{10}}x^{10}

What is the first derivative of xe^{-x^{10}} ?

The first derivative of xe^{-x^{10}} is e^{-x^{10}}-10e^{-x^{10}}x^{10}

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derivative of

x e^{- x^{10}}

e^{- x^{10}} - 10 e^{- x^{10}} x^{10}

Solution steps

\frac{d}{d x} (x e^{- x^{10}})

Apply the Product Rule:

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

f = x, g = e^{- x^{10}}

= \frac{d x}{d x} e^{- x^{10}} + \frac{d}{d x} (e^{- x^{10}}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{- x^{10}}) = - 10 e^{- x^{10}} x^{9}

= 1 \cdot e^{- x^{10}} + (- 10 e^{- x^{10}} x^{9}) x

Simplify

1 \cdot e^{- x^{10}} + (- 10 e^{- x^{10}} x^{9}) x : e^{- x^{10}} - 10 e^{- x^{10}} x^{10}

= e^{- x^{10}} - 10 e^{- x^{10}} x^{10}

y^{^{'}} - 2 y = - 4 y^{3}

\int x^{3} e^{2} d x

\int (1 + t)^{2} d t

\frac{2}{x + 5}, at x = 4

f (x) = 2 x^{2} - x - 3, at x = 1

What is the derivative of xe^{-x^{10}} ?
The derivative of xe^{-x^{10}} is e^{-x^{10}}-10e^{-x^{10}}x^{10}
What is the first derivative of xe^{-x^{10}} ?
The first derivative of xe^{-x^{10}} is e^{-x^{10}}-10e^{-x^{10}}x^{10}