Solve z=x^2+y^2 - ScanMath

Simplify

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

Find the first partial derivative by treating the variable y as a constant and differentiating with respect to x

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

Use differentiation rule \frac{\partial}{\partial x} (f (x) \pm g (x)) = \frac{\partial}{\partial x} (f (x)) \pm \frac{\partial}{\partial x} (g (x))

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

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

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

Use \frac{\partial}{\partial x} (c) = 0 to find derivative

\frac{\partial z}{\partial x} = 2 x + 0

Solution

\frac{\partial z}{\partial x} = 2 x

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