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

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

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

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

2 e^{y} x

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (y^{2}) = 0

= e^{y} (2 x - 0)

Simplify

= 2 e^{y} x

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