What is (\partial)/(\partial x)(ln(x+8y+7z)) ?

The answer to (\partial)/(\partial x)(ln(x+8y+7z)) is 1/(x+8y+7z)

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(\partial)/(\partial x)(ln(x+8y+7z))

\frac{\partial}{\partial x} (ln (x + 8 y + 7 z))

\frac{1}{x + 8 y + 7 z}

Solution steps

\frac{\partial}{\partial x} (ln (x + 8 y + 7 z))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{x + 8 y + 7 z} \frac{\partial}{\partial x} (x + 8 y + 7 z)

= \frac{1}{x + 8 y + 7 z} \frac{\partial}{\partial x} (x + 8 y + 7 z)

\frac{\partial}{\partial x} (x + 8 y + 7 z) = 1

= \frac{1}{x + 8 y + 7 z} \cdot 1

Simplify

= \frac{1}{x + 8 y + 7 z}

\int (\frac{1}{t ^{2}} + t) d t

\int (\frac{7}{x} - \frac{3}{x ^{2}}) d x

\int (3 x^{5} - 8)^{9} 6 x^{4} d x

y^{^{'}} = \frac{x y ^{3}}{( 1 + x ^{2} ) ^{\frac{1}{2}}}

\frac{d}{d x} (arctan (\frac{a}{x}))

What is (\partial)/(\partial x)(ln(x+8y+7z)) ?
The answer to (\partial)/(\partial x)(ln(x+8y+7z)) is 1/(x+8y+7z)