What is (\partial)/(\partial x)(Ax+By+Cx^2y) ?

The answer to (\partial)/(\partial x)(Ax+By+Cx^2y) is A+2xyC

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(\partial)/(\partial x)(Ax+By+Cx^2y)

\frac{\partial}{\partial x} (A x + B y + C x^{2} y)

A + 2 x y C

Solution steps

\frac{\partial}{\partial x} (A x + B y + C x^{2} y)

Treat

A, B, y, C

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (A x) + \frac{\partial}{\partial x} (B y) + \frac{\partial}{\partial x} (C x^{2} y)

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

\frac{\partial}{\partial x} (B y) = 0

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

= A + 0 + 2 y C x

Simplify

= A + 2 x y C

5 t^{2}

x \to - 6 - lim (\frac{∣ x + 6 ∣}{x + 6})

\int_{0}^{1} (x^{2} + 1) d x

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

\frac{d y}{d x} = \frac{3 x - 9}{2 x + 8}

What is (\partial)/(\partial x)(Ax+By+Cx^2y) ?
The answer to (\partial)/(\partial x)(Ax+By+Cx^2y) is A+2xyC