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

The answer to (\partial)/(\partial y)(xzln(x+y+z)) is (xz)/(x+y+z)

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

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d ^{2}}{d x ^{2}} (5 cos (2 x + 10))

q \to 18 lim (0.9 q^{2} - 6 q + 80)

sec (θ) (θ - tan (θ))

x^{2} + 8

f (x) = x^{2} - 10 x + 34 + x^{2} + 16

What is (\partial)/(\partial y)(xzln(x+y+z)) ?
The answer to (\partial)/(\partial y)(xzln(x+y+z)) is (xz)/(x+y+z)