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

The answer to (\partial)/(\partial x)(5x^2y-x+3y^3) is 10xy-1

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

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

10 x y - 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (5 x^{2} y) = 10 y x

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

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

= 10 y x - 1 + 0

Simplify

= 10 x y - 1

\int \frac{5 x}{x ^{2} + 8} d x

x \to 4 lim (x + 5 - 3)

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

\int (\frac{1}{1 + cos ( x )}) d x

x \to 0 lim (x^{2} c x c x)

What is (\partial)/(\partial x)(5x^2y-x+3y^3) ?
The answer to (\partial)/(\partial x)(5x^2y-x+3y^3) is 10xy-1