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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

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

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

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

\frac{\partial}{\partial y} (y) = 1

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

= 1 \cdot e^{x^{2} - y} + (- e^{x^{2} - y}) y

Simplify

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

\int x (sin (x^{\frac{3}{2}} - 1))^{2} d x

\frac{d}{d x} ((2 x^{2} - 7 x + 6)^{2})

7

f (x) = 6 - x

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