What is (\partial)/(\partial x)((z)(5xy-4x+5y^3)) ?

The answer to (\partial)/(\partial x)((z)(5xy-4x+5y^3)) is z(5y-4)

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(\partial)/(\partial x)((z)(5xy-4x+5y^3))

\frac{\partial}{\partial x} ((z) (5 x y - 4 x + 5 y^{3}))

z (5 y - 4)

Solution steps

\frac{\partial}{\partial x} ((z) (5 x y - 4 x + 5 y^{3}))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (5 x y - 4 x + 5 y^{3})

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (5 x y) - \frac{\partial}{\partial x} (4 x) + \frac{\partial}{\partial x} (5 y^{3}))

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

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

\frac{\partial}{\partial x} (5 y^{3}) = 0

= z (5 y - 4 + 0)

Simplify

= z (5 y - 4)

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

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

e^{(x + i y)^{2}}

(- e^{x} sin (x) + e^{x} cos (x))^{2}

\frac{1}{( 1 + x ) ^{4}}

What is (\partial)/(\partial x)((z)(5xy-4x+5y^3)) ?
The answer to (\partial)/(\partial x)((z)(5xy-4x+5y^3)) is z(5y-4)