What is (\partial)/(\partial y)(ln(x+8y+5z)) ?

The answer to (\partial)/(\partial y)(ln(x+8y+5z)) is 8/(x+8y+5z)

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(\partial)/(\partial y)(ln(x+8y+5z))

\frac{\partial}{\partial y} (ln (x + 8 y + 5 z))

\frac{8}{x + 8 y + 5 z}

Solution steps

\frac{\partial}{\partial y} (ln (x + 8 y + 5 z))

Treat

x, z

as constants

Apply the chain rule:

\frac{1}{x + 8 y + 5 z} \frac{\partial}{\partial y} (x + 8 y + 5 z)

= \frac{1}{x + 8 y + 5 z} \frac{\partial}{\partial y} (x + 8 y + 5 z)

\frac{\partial}{\partial y} (x + 8 y + 5 z) = 8

= \frac{1}{x + 8 y + 5 z} \cdot 8

Simplify

\frac{1}{x + 8 y + 5 z} \cdot 8 : \frac{8}{x + 8 y + 5 z}

= \frac{8}{x + 8 y + 5 z}

\frac{d y}{d x} - 2 x y = - 6 x^{2} e^{x^{2}}

x \to 0 lim (\frac{sin ( c ) x}{x})

x \to 0 + lim (x^{x^{3}})

n = 1 \sum \infty \frac{( 1 ) ^{n}}{n}

n = 0 \sum \infty \frac{17}{2}

What is (\partial)/(\partial y)(ln(x+8y+5z)) ?
The answer to (\partial)/(\partial y)(ln(x+8y+5z)) is 8/(x+8y+5z)