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

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

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

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

2 z x

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= z (2 x + 0)

Simplify

= 2 z x

(x^{3} + 3 x - 2 x^{2} - 6) + i (- 2 x^{2} + 4 x)

in (\frac{e x ^{2}}{y})

(\frac{1}{x} + y) (\frac{1}{x} - y)

(e^{x i} - cos (x))^{2}

(\frac{6}{7} - x)^{5}

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