What is (\partial)/(\partial x)((y)(x+4y)) ?

The answer to (\partial)/(\partial x)((y)(x+4y)) is y

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(\partial)/(\partial x)((y)(x+4y))

\frac{\partial}{\partial x} ((y) (x + 4 y))

y

Solution steps

\frac{\partial}{\partial x} ((y) (x + 4 y))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} (x + 4 y)

Apply the Sum/Difference Rule:

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

= y (\frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (4 y))

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

\frac{\partial}{\partial x} (4 y) = 0

= y (1 + 0)

Simplify

= y

\frac{1}{( x ^{3} + x ^{2} ) ^{3}}

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[(x - 2) e^{x}]

What is (\partial)/(\partial x)((y)(x+4y)) ?
The answer to (\partial)/(\partial x)((y)(x+4y)) is y