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

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

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

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

2 x e^{x - y} + e^{x - y} x^{2}

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

= 2 x e^{x - y} + e^{x - y} x^{2}

\frac{d x}{d t} = 2 t e^{2 x}

\frac{d}{d x} (16 - \frac{1}{625} x^{2})

2^{80}

x^{2} + y^{2} = 9

\int_{1}^{4} 6 x d x

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