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

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

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

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

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

Solution steps

\frac{\partial}{\partial x} ((x^{2} - 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} - 2, g = e^{x^{2} y}

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

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

\int \frac{30}{30 + e ^{x}} d x

y = 4 (6 - x^{2})^{5}

\int 4 m (9 m^{2} - 10 m) d m

ln (15 x)

f (x) = x^{12}

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