What is (\partial)/(\partial x)((z)(x^2+3xy-y^2)) ?

The answer to (\partial)/(\partial x)((z)(x^2+3xy-y^2)) is z(2x+3y)

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(\partial)/(\partial x)((z)(x^2+3xy-y^2))

\frac{\partial}{\partial x} ((z) (x^{2} + 3 x y - y^{2}))

z (2 x + 3 y)

Solution steps

\frac{\partial}{\partial x} ((z) (x^{2} + 3 x y - y^{2}))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (x^{2} + 3 x y - y^{2})

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (3 x y) - \frac{\partial}{\partial x} (y^{2}))

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

\frac{\partial}{\partial x} (3 x y) = 3 y

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

= z (2 x + 3 y - 0)

Simplify

= z (2 x + 3 y)

sin (a) (1 - cos (b)) + sin (b) (1 - cos (a))

(3 x - 4 y + 4 = 0,) (9 x - 12 y - 4 = 0)

2 (3 + 5)

4 (\frac{1}{2} x + \frac{3}{2} y)

lo g_{10} (x y z)

What is (\partial)/(\partial x)((z)(x^2+3xy-y^2)) ?
The answer to (\partial)/(\partial x)((z)(x^2+3xy-y^2)) is z(2x+3y)