What is (\partial)/(\partial x)(5x^2y-5x+4y^3) ?

The answer to (\partial)/(\partial x)(5x^2y-5x+4y^3) is 10xy-5

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(\partial)/(\partial x)(5x^2y-5x+4y^3)

\frac{\partial}{\partial x} (5 x^{2} y - 5 x + 4 y^{3})

10 x y - 5

Solution steps

\frac{\partial}{\partial x} (5 x^{2} y - 5 x + 4 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} (5 x) + \frac{\partial}{\partial x} (4 y^{3})

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

\frac{\partial}{\partial x} (5 x) = 5

\frac{\partial}{\partial x} (4 y^{3}) = 0

= 10 y x - 5 + 0

Simplify

= 10 x y - 5

\int x^{2} (e^{x}) d x

x \to - 2 lim (\frac{2 x + 2}{x - 1})

\frac{6 x}{1 - tan ( x )}

\int \frac{x - 3}{x + 1} d x

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

What is (\partial)/(\partial x)(5x^2y-5x+4y^3) ?
The answer to (\partial)/(\partial x)(5x^2y-5x+4y^3) is 10xy-5