What is (\partial)/(\partial y)(x^2e^{y^2}) ?

The answer to (\partial)/(\partial y)(x^2e^{y^2}) is x^2e^{y^2}*2y

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(\partial)/(\partial y)(x^2e^{y^2})

\frac{\partial}{\partial y} (x^{2} e^{y^{2}})

x^{2} e^{y^{2}} \cdot 2 y

Solution steps

\frac{\partial}{\partial y} (x^{2} e^{y^{2}})

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= x^{2} \frac{\partial}{\partial y} (e^{y^{2}})

Apply the chain rule:

e^{y^{2}} \frac{\partial}{\partial y} (y^{2})

= e^{y^{2}} \frac{\partial}{\partial y} (y^{2})

\frac{\partial}{\partial y} (y^{2}) = 2 y

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

\frac{d}{d x} (5 x^{3} 5 x - 2)

\int 1 - x^{2} + \frac{1}{2} x^{4} d x

x^{3} - 2 x^{2} + 3 x - 5, 2

x \to 4 lim (2 x^{2} - 11 x)

\frac{d}{d x} (\frac{42}{x ^{4}})

What is (\partial)/(\partial y)(x^2e^{y^2}) ?
The answer to (\partial)/(\partial y)(x^2e^{y^2}) is x^2e^{y^2}*2y