What is (\partial)/(\partial x)(ln(x+9y+8z)) ?

The answer to (\partial)/(\partial x)(ln(x+9y+8z)) is 1/(x+9y+8z)

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(\partial)/(\partial x)(ln(x+9y+8z))

\frac{\partial}{\partial x} (ln (x + 9 y + 8 z))

\frac{1}{x + 9 y + 8 z}

Solution steps

\frac{\partial}{\partial x} (ln (x + 9 y + 8 z))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{x + 9 y + 8 z} \frac{\partial}{\partial x} (x + 9 y + 8 z)

= \frac{1}{x + 9 y + 8 z} \frac{\partial}{\partial x} (x + 9 y + 8 z)

\frac{\partial}{\partial x} (x + 9 y + 8 z) = 1

= \frac{1}{x + 9 y + 8 z} \cdot 1

Simplify

= \frac{1}{x + 9 y + 8 z}

\frac{\partial}{\partial x} (x y^{2} z^{4})

\int_{2}^{1} - 4 x^{- 3} d x

\int \frac{x ^{7}}{( 2 - x ^{8} ) ^{2}} d x

10000 y^{^{''}} - 81 y = 0, y (0) = 1, y^{^{'}} (0) = 3

\frac{\partial}{\partial y} (\frac{y ^{3}}{x ^{2}})

What is (\partial)/(\partial x)(ln(x+9y+8z)) ?
The answer to (\partial)/(\partial x)(ln(x+9y+8z)) is 1/(x+9y+8z)