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

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

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

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

x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= x + 0

Simplify

= x

f (x) = 5 e x

\frac{d}{d t} (t^{\frac{1}{2}})

x \to 0 lim (\frac{( 3 + x ^{2} ) - 9}{x})

\frac{d}{d x} ((2 x^{2} + x + 9)^{- 3})

\int \frac{1 - x ^{2}}{x + x ^{3}} d x

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