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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

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