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

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

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

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

\frac{z}{2 x + y}

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= z \frac{1}{2 x + y} \cdot 1

Simplify

z \frac{1}{2 x + y} \cdot 1 : \frac{z}{2 x + y}

= \frac{z}{2 x + y}

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

\frac{d}{d x} (\frac{x ^{2} - 7 x + 13}{x - 3})

y^{^{''}} - 2 y^{^{'}} = 4 t

\frac{d}{d x} (\frac{x}{10})

x \to 10 + lim (\frac{x ^{3}}{x - 10})

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