What is (\partial)/(\partial x)((z)(x^2y+4x+3y)) ?

The answer to (\partial)/(\partial x)((z)(x^2y+4x+3y)) is z(2xy+4)

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(\partial)/(\partial x)((z)(x^2y+4x+3y))

\frac{\partial}{\partial x} ((z) (x^{2} y + 4 x + 3 y))

z (2 x y + 4)

Solution steps

\frac{\partial}{\partial x} ((z) (x^{2} y + 4 x + 3 y))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (x^{2} y + 4 x + 3 y)

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial x} (4 x) + \frac{\partial}{\partial x} (3 y))

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

\frac{\partial}{\partial x} (4 x) = 4

\frac{\partial}{\partial x} (3 y) = 0

= z (2 y x + 4 + 0)

Simplify

= z (2 x y + 4)

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

(x + 5)^{4}

(x^{2} - \frac{1}{x ^{2}}) (x^{2} + \frac{1}{x ^{2}})

(cos (β) - 1) (sin (β) - 1)

(s + 170) (s^{2} - 2025) (s + 20 π)

What is (\partial)/(\partial x)((z)(x^2y+4x+3y)) ?
The answer to (\partial)/(\partial x)((z)(x^2y+4x+3y)) is z(2xy+4)