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

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

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

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

2 x + y

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = x + y

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

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

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

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

Simplify

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

= 2 x + y

\int_{- \infty}^{2} \frac{1}{x ^{2} + 1} d x

\frac{\partial}{\partial y} (e^{x} + yz)

\int \frac{1}{e ^{z} + e ^{- z}} d z

\frac{d}{d x} ((3 + x - 2 x^{2})^{\frac{1}{4}})

\frac{d y}{d x}, 4 x^{2} + 9 y^{2} = 36

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