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Popular >

derivative of xe^{x^3}

Solution

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

Solution

e^{x^{3}} + 3 e^{x^{3}} x^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 1 \cdot e^{x^{3}} + e^{x^{3}} \cdot 3 x^{2} x

Simplify

1 \cdot e^{x^{3}} + e^{x^{3}} \cdot 3 x^{2} x : e^{x^{3}} + 3 e^{x^{3}} x^{3}

= e^{x^{3}} + 3 e^{x^{3}} x^{3}

Graph

Popular Examples

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x^{2} y^{^{'}} - 2 x^{3} e^{- \frac{1}{x}} = y

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derivative of (7x^2+2)(6x+sqrt(x))derivative of

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Frequently Asked Questions (FAQ)

What is the derivative of xe^{x^3} ?
The derivative of xe^{x^3} is e^{x^3}+3e^{x^3}x^3
What is the first derivative of xe^{x^3} ?
The first derivative of xe^{x^3} is e^{x^3}+3e^{x^3}x^3