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

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

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

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

z (3 x^{2} + 2 y x)

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

(y + Δ y)^{4} - 2 (y + Δ y)^{3}

\frac{1}{1 - 2 x ^{3}}

x^{2} (0, 2) y (3, - 3)

(4 \cdot 0.2) + (\frac{1}{5}) - (1 - 0.9) \cdot (\frac{1}{2})

\frac{7}{( x + 3 ) ^{2}}

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