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

The answer to (\partial)/(\partial x)(ax+by^2+cx^2y) is a+2xyc

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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 x yc

Solution steps

\frac{\partial}{\partial x} (a x + b y^{2} + 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^{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 yc x

= a + 0 + 2 yc x

Simplify

= a + 2 x yc

\frac{d}{d x} (arctan (tan (x)))

x \to 0 + lim (x ln (x^{2}))

y = 9 - x^{2}, y = 0, x

\frac{d}{d x} (\frac{( 3 x - 1 )}{x ^{\frac{2}{3}}})

\frac{\partial}{\partial x} (4 + x ln (x y - 5))

What is (\partial)/(\partial x)(ax+by^2+cx^2y) ?
The answer to (\partial)/(\partial x)(ax+by^2+cx^2y) is a+2xyc