What is (\partial)/(\partial x)(x(x+3y+2)) ?

The answer to (\partial)/(\partial x)(x(x+3y+2)) is 2x+3y+2

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(\partial)/(\partial x)(x(x+3y+2))

\frac{\partial}{\partial x} (x (x + 3 y + 2))

2 x + 3 y + 2

Solution steps

\frac{\partial}{\partial x} (x (x + 3 y + 2))

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = x + 3 y + 2

= \frac{\partial}{\partial x} (x) (x + 3 y + 2) + \frac{\partial}{\partial x} (x + 3 y + 2) x

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

\frac{\partial}{\partial x} (x + 3 y + 2) = 1

= 1 \cdot (x + 3 y + 2) + 1 \cdot x

Simplify

1 \cdot (x + 3 y + 2) + 1 \cdot x : 2 x + 3 y + 2

= 2 x + 3 y + 2

\frac{d y}{d x} = 20 + 28 x + 40 y + 56 x y

\int \frac{1}{8} sin (8 x) d x

\int \frac{5}{x} d x

g (x) = 6 x + 8

\int 2 x - y d x

What is (\partial)/(\partial x)(x(x+3y+2)) ?
The answer to (\partial)/(\partial x)(x(x+3y+2)) is 2x+3y+2