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

The derivative of x^2e^{x^2} is 2e^{x^2}x+2e^{x^2}x^3

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

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

\frac{d}{d x} (x^{2} ln (4 x))

\int \frac{4 + x}{16 - x ^{2}} d x

\int \frac{1}{2 + x} d x

t^{2} y^{^{''}} + t y^{^{'}} + 25 y = 0

\frac{d y}{d x} = 3 x

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