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

The answer to (\partial)/(\partial x)(x^2+y^2-z) is 2x

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(\partial)/(\partial x)(x^2+y^2-z)

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

2 x

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (z) = 0

= 2 x + 0 - 0

Simplify

= 2 x

\int 3 - \frac{1}{3} \cdot (x - 4)^{2} d x

\int \frac{3 x ^{2} + 1}{( x ^{2} + 1 ) ^{3}} d x

\int_{0}^{2} \frac{x ^{2} - 2}{x + 1} d x

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (0) = 4, y^{^{'}} (0) = 0

\frac{d}{d x} (cos^{7} (x))

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