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

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

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

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

2 x e^{x^{2} y} + e^{x^{2} y} \cdot 2 y x (x^{2} + y^{2})

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

= 2 x e^{x^{2} y} + e^{x^{2} y} \cdot 2 y x (x^{2} + y^{2})

\frac{x}{( x ^{2} - 1 )}

\int sin (x) e^{2 x} d x

f (x) = x, (25, 5)

\int (u - 2)^{3} ln (u - 2) d u

\frac{d}{d x} (\frac{x + 7}{x})

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