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

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

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

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

3 y - 10 y x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 3 y - 10 y x

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

\int \frac{5}{x ( x - 5 ) ^{2}} d x

f (t) = sin (4 t)

x \to π lim (x sec (x))

\int_{- 2}^{- 1} 4 x^{3} + \frac{2}{x ^{3}} d x

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