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

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

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(\partial)/(\partial x)((x)^2+(y)^4)

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

2 x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 x + 0

Simplify

= 2 x

\frac{x ^{3}}{e ^{\frac{1}{x}}}

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

\frac{\partial}{\partial x} (\frac{y - 5 x}{y ^{2} + 4 x ^{2}})

\frac{\partial}{\partial x} (x^{0.5} y)

y^{^{''}} - y^{^{'}} - 6 y = 0, y (0) = 1, y^{^{'}} (0) = 4

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