What is (\partial)/(\partial x)(Ax+by^2+cx^2y) ?

The answer to (\partial)/(\partial x)(Ax+by^2+cx^2y) is A+2cxy

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(\partial)/(\partial x)(Ax+by^2+cx^2y)

\frac{\partial}{\partial x} (A x + b y^{2} + c x^{2} y)

A + 2 c x y

Solution steps

\frac{\partial}{\partial x} (A x + b y^{2} + c x^{2} y)

Treat

A, b, c, y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (A x) + \frac{\partial}{\partial x} (b y^{2}) + \frac{\partial}{\partial x} (c x^{2} y)

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

\frac{\partial}{\partial x} (b y^{2}) = 0

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

= A + 0 + 2 cy x

Simplify

= A + 2 c x y

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What is (\partial)/(\partial x)(Ax+by^2+cx^2y) ?
The answer to (\partial)/(\partial x)(Ax+by^2+cx^2y) is A+2cxy