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

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

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

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

y e^{x^{2} - x y} (2 x - y)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= y e^{x^{2} - x y} (2 x - y)

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