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

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

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

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

e^{x + y^{2}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x + y^{2}) = 1

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

Simplify

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

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