What is (\partial)/(\partial x)((z)(3x+5xy-2y^2)) ?

The answer to (\partial)/(\partial x)((z)(3x+5xy-2y^2)) is z(5y+3)

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(\partial)/(\partial x)((z)(3x+5xy-2y^2))

\frac{\partial}{\partial x} ((z) (3 x + 5 x y - 2 y^{2}))

z (5 y + 3)

Solution steps

\frac{\partial}{\partial x} ((z) (3 x + 5 x y - 2 y^{2}))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (3 x + 5 x y - 2 y^{2})

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (3 x) + \frac{\partial}{\partial x} (5 x y) - \frac{\partial}{\partial x} (2 y^{2}))

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

\frac{\partial}{\partial x} (5 x y) = 5 y

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

= z (3 + 5 y - 0)

Simplify

= z (5 y + 3)

\frac{x + 3}{( x - 5 ) ( x - 3 )}

(3 x - 5 5 y^{2} - 3 x + 19 + 5)^{2}

\frac{a ( a ^{2} - 4 ) ^{3}}{8}

(4 sin (3 x) csc (2 x) - 3 tan (x)) csc (x) - 4

\frac{2 X ^{3} + X + 3}{( X ^{2} + 1 ) ^{2}}

What is (\partial)/(\partial x)((z)(3x+5xy-2y^2)) ?
The answer to (\partial)/(\partial x)((z)(3x+5xy-2y^2)) is z(5y+3)