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

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

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(\partial}{\partial x}(\frac{x^2)/2+y^4)

\frac{\partial}{\partial x} (\frac{x ^{2}}{2} + y^{4})

x

Solution steps

\frac{\partial}{\partial x} (\frac{x ^{2}}{2} + y^{4})

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} (y^{4})

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

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

= x + 0

Simplify

= x

\frac{d}{d x} (x^{4} + 2 x^{2} - x)

\frac{\partial}{\partial x} (1 x)

(1 + y) \frac{d y}{d t} = 6 t, y (2) = 5

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

\int \frac{( x + 1 )}{x ^{2} + 2 x} d x

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