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

The answer to (\partial)/(\partial x)(5xy-3x^2y) is 5y-6yx

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

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

5 y - 6 y x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (3 x^{2} y) = 6 y x

= 5 y - 6 y x

\int x^{4} cos (x^{5}) d x

x \to 2 lim (\frac{2}{x} + 4)

\int_{0}^{4} \frac{2}{x} d x

\int (7 e^{9 x}) d x

5^{t a n (5 x)}

What is (\partial)/(\partial x)(5xy-3x^2y) ?
The answer to (\partial)/(\partial x)(5xy-3x^2y) is 5y-6yx