What is (\partial)/(\partial x)(2xy(x+y)+x^2+2x) ?

The answer to (\partial)/(\partial x)(2xy(x+y)+x^2+2x) is 2y(2x+y)+2x+2

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(\partial)/(\partial x)(2xy(x+y)+x^2+2x)

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

2 y (2 x + y) + 2 x + 2

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x y (x + y)) = 2 y (2 x + y)

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

\frac{\partial}{\partial x} (2 x) = 2

= 2 y (2 x + y) + 2 x + 2

\frac{\partial}{\partial y} (ln (x^{2} y))

7 \cdot ln (x)

sin^{3} (3 x)

\frac{\partial}{\partial y} (- 2 cos (y))

\frac{\partial}{\partial x} (x^{4} - y^{2})

What is (\partial)/(\partial x)(2xy(x+y)+x^2+2x) ?
The answer to (\partial)/(\partial x)(2xy(x+y)+x^2+2x) is 2y(2x+y)+2x+2