What is (\partial)/(\partial x)(ln(x+9y+2z)) ?

The answer to (\partial)/(\partial x)(ln(x+9y+2z)) is 1/(x+9y+2z)

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(\partial)/(\partial x)(ln(x+9y+2z))

\frac{\partial}{\partial x} (ln (x + 9 y + 2 z))

\frac{1}{x + 9 y + 2 z}

Solution steps

\frac{\partial}{\partial x} (ln (x + 9 y + 2 z))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{x + 9 y + 2 z} \frac{\partial}{\partial x} (x + 9 y + 2 z)

= \frac{1}{x + 9 y + 2 z} \frac{\partial}{\partial x} (x + 9 y + 2 z)

\frac{\partial}{\partial x} (x + 9 y + 2 z) = 1

= \frac{1}{x + 9 y + 2 z} \cdot 1

Simplify

= \frac{1}{x + 9 y + 2 z}

\frac{d}{d x} (2 tan (x + \frac{π}{12}))

\frac{d}{d x} ((x + 1)^{\frac{2}{3}} (3 x^{2} - 2)^{3})

\int (sec (2 x) tan (2 x)) d x

\int \frac{m ^{3}}{( z ^{2} ) ^{3}} d m

x \to 6 lim (\frac{x}{6 - x})

What is (\partial)/(\partial x)(ln(x+9y+2z)) ?
The answer to (\partial)/(\partial x)(ln(x+9y+2z)) is 1/(x+9y+2z)