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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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