What is (\partial)/(\partial x)(x*Y(x)) ?

The answer to (\partial)/(\partial x)(x*Y(x)) is {Y}(x)+x(\partial)/(\partial x)({Y}(x))

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(\partial)/(\partial x)(x*Y(x))

\frac{\partial}{\partial x} (x \cdot Y (x))

Y (x) + x \frac{\partial}{\partial x} (Y (x))

Solution steps

\frac{\partial}{\partial x} (x Y (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = Y (x)

= \frac{\partial}{\partial x} (x) Y (x) + \frac{\partial}{\partial x} (Y (x)) x

\frac{\partial}{\partial x} (x) = 1

= 1 \cdot Y (x) + \frac{\partial}{\partial x} (Y (x)) x

Simplify

= Y (x) + x \frac{\partial}{\partial x} (Y (x))

What is (\partial)/(\partial x)(x*Y(x)) ?
The answer to (\partial)/(\partial x)(x*Y(x)) is {Y}(x)+x(\partial)/(\partial x)({Y}(x))