What is (\partial)/(\partial u)(x^5v^2+2y^3u-3) ?

The answer to (\partial)/(\partial u)(x^5v^2+2y^3u-3) is 2y^3

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(\partial)/(\partial u)(x^5v^2+2y^3u-3)

\frac{\partial}{\partial u} (x^{5} v^{2} + 2 y^{3} u - 3)

2 y^{3}

Solution steps

\frac{\partial}{\partial u} (x^{5} v^{2} + 2 y^{3} u - 3)

Treat

x, v, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial u} (x^{5} v^{2}) + \frac{\partial}{\partial u} (2 y^{3} u) - \frac{\partial}{\partial u} (3)

\frac{\partial}{\partial u} (x^{5} v^{2}) = 0

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

\frac{\partial}{\partial u} (3) = 0

= 0 + 2 y^{3} - 0

Simplify

= 2 y^{3}

\frac{\partial}{\partial x} (61 - x^{2} - 3 y^{2})

\int_{2}^{5} x^{2} d x

x \to 0 + lim (7 sin (x) ln (x))

\int sin (11 x) ln (sin (11 x)) d x

f (x) = x^{3} - 2 x + 1, at x = 0

What is (\partial)/(\partial u)(x^5v^2+2y^3u-3) ?
The answer to (\partial)/(\partial u)(x^5v^2+2y^3u-3) is 2y^3