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Popular >

derivative of x^3e^{x^2}

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

e^{x^{2}} \cdot 2 x x^{3} = 2 e^{x^{2}} x^{4}

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

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Frequently Asked Questions (FAQ)

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