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

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

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

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

x^{2} C + 2 B y

Solution steps

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

Treat

A, x, B, C

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (B y^{2}) = 2 B y

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

= 0 + 2 B y + x^{2} C

Simplify

= x^{2} C + 2 B y

y d x + (y - x) d y = 0

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\int \frac{1}{x + 5} d x

\int \frac{1}{t ^{2}} sin (\frac{2}{1} + 3) d t

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