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

The answer to (\partial)/(\partial x)((e^{x^2}+e^{y^2})^2) is 4e^{x^2}x(e^{x^2}+e^{y^2})

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

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

4 e^{x^{2}} x (e^{x^{2}} + e^{y^{2}})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= 4 e^{x^{2}} x (e^{x^{2}} + e^{y^{2}})

What is (\partial)/(\partial x)((e^{x^2}+e^{y^2})^2) ?
The answer to (\partial)/(\partial x)((e^{x^2}+e^{y^2})^2) is 4e^{x^2}x(e^{x^2}+e^{y^2})