What is (\partial)/(\partial y)(ln(x+6y+5z)) ?

The answer to (\partial)/(\partial y)(ln(x+6y+5z)) is 6/(x+6y+5z)

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(\partial)/(\partial y)(ln(x+6y+5z))

\frac{\partial}{\partial y} (ln (x + 6 y + 5 z))

\frac{6}{x + 6 y + 5 z}

Solution steps

\frac{\partial}{\partial y} (ln (x + 6 y + 5 z))

Treat

x, z

as constants

Apply the chain rule:

\frac{1}{x + 6 y + 5 z} \frac{\partial}{\partial y} (x + 6 y + 5 z)

= \frac{1}{x + 6 y + 5 z} \frac{\partial}{\partial y} (x + 6 y + 5 z)

\frac{\partial}{\partial y} (x + 6 y + 5 z) = 6

= \frac{1}{x + 6 y + 5 z} \cdot 6

Simplify

\frac{1}{x + 6 y + 5 z} \cdot 6 : \frac{6}{x + 6 y + 5 z}

= \frac{6}{x + 6 y + 5 z}

\int \frac{10}{( x + 1 ) ( x ^{2} + 9 ) ^{2}} d x

x \to 8 - lim (\frac{x - 8}{∣ x - 8 ∣})

\frac{d}{d x} (2 (4 - 9 x)^{4})

(x y + y + y^{2}) d x + (x + 2 y) d y = 0

f (x) = x - 5, at x = 6

What is (\partial)/(\partial y)(ln(x+6y+5z)) ?
The answer to (\partial)/(\partial y)(ln(x+6y+5z)) is 6/(x+6y+5z)