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

The answer to (\partial)/(\partial x)(x^5v^2+2y^3u-3) is 5x^4v^2

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

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

5 x^{4} v^{2}

Solution steps

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

Treat

v, y, u

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x^{5} v^{2}) = 5 v^{2} x^{4}

\frac{\partial}{\partial x} (2 y^{3} u) = 0

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

= 5 v^{2} x^{4} + 0 - 0

Simplify

= 5 x^{4} v^{2}

\int y^{\frac{1}{3}} d y

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

\int 5 + cos (x) d x

32 y^{^{''}} + 20 y^{^{'}} - 3 y = 0

\int 5 e^{u} d u

What is (\partial)/(\partial x)(x^5v^2+2y^3u-3) ?
The answer to (\partial)/(\partial x)(x^5v^2+2y^3u-3) is 5x^4v^2