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

The answer to (\partial)/(\partial x)(wsqrt(x+2y+3z)) is w/(2sqrt(x+2y+3z))

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

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

\frac{w}{2 x + 2 y + 3 z}

Solution steps

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

Treat

w, y, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= w \frac{1}{2 x + 2 y + 3 z} \cdot 1

Simplify

w \frac{1}{2 x + 2 y + 3 z} \cdot 1 : \frac{w}{2 x + 2 y + 3 z}

= \frac{w}{2 x + 2 y + 3 z}

x \to 2 lim (\frac{[ x - 2 ]}{x - 2})

\frac{d}{d x} (\frac{a ^{2} - x ^{3}}{b ^{2}})

x = 7 y^{2}, x = 8 + 5 y^{2}

\frac{2 x}{x + 2}

\int \frac{x ^{2} + 1}{x ^{2}} d x

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