What is (\partial}{\partial x}(\frac{x^3)/3+4y) ?

The answer to (\partial}{\partial x}(\frac{x^3)/3+4y) is x^2

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

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

x^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (4 y) = 0

= x^{2} + 0

Simplify

= x^{2}

\frac{d y}{d x} = x^{6} y^{- 7}

1 - y^{2}

\frac{d y}{d x} = x^{8} e^{x^{9}}

y^{^{''}} + 25 y = - 10 sin (5 t)

x \to a + 1 lim (x^{2} - 1)

What is (\partial}{\partial x}(\frac{x^3)/3+4y) ?
The answer to (\partial}{\partial x}(\frac{x^3)/3+4y) is x^2