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

The answer to (\partial)/(\partial x)(5xy-4x^2y) is 5y-8yx

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

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

5 y - 8 y x

Solution steps

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

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

\frac{\partial}{\partial x} (4 x^{2} y) = 8 y x

= 5 y - 8 y x

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

x \to 0 lim (sin^{4} (x))

cos (2 (t - \frac{5 π}{2}))

(2.3) (1.3)

\int \frac{x}{1 + x ^{4}} d x

What is (\partial)/(\partial x)(5xy-4x^2y) ?
The answer to (\partial)/(\partial x)(5xy-4x^2y) is 5y-8yx