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

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

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

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

\frac{x + y}{x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

2 (x + y) \frac{1}{2 x} : \frac{x + y}{x}

= \frac{x + y}{x}

\int 2 (2 x + 8)^{4} d x

\int_{0}^{π} 4 x cos (x^{2}) d x

\frac{d x}{d t} = x - 1

\int \frac{1}{( 1 + x ) ^{4}} d x

x \to \frac{π}{2} lim (cot (x))

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