What is (\partial)/(\partial x)(ln(3x+6y+9z)) ?

The answer to (\partial)/(\partial x)(ln(3x+6y+9z)) is 1/(x+2y+3z)

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(\partial)/(\partial x)(ln(3x+6y+9z))

\frac{\partial}{\partial x} (ln (3 x + 6 y + 9 z))

\frac{1}{x + 2 y + 3 z}

Solution steps

\frac{\partial}{\partial x} (ln (3 x + 6 y + 9 z))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{3 x + 6 y + 9 z} \frac{\partial}{\partial x} (3 x + 6 y + 9 z)

= \frac{1}{3 x + 6 y + 9 z} \frac{\partial}{\partial x} (3 x + 6 y + 9 z)

\frac{\partial}{\partial x} (3 x + 6 y + 9 z) = 3

= \frac{1}{3 x + 6 y + 9 z} \cdot 3

Simplify

\frac{1}{3 x + 6 y + 9 z} \cdot 3 : \frac{1}{x + 2 y + 3 z}

= \frac{1}{x + 2 y + 3 z}

\frac{d y}{d x} = x e^{x + y}

\frac{7 x ^{2} + 1}{x ^{2} + 5}

\frac{d}{d x} (7 cot (x))

x \to \infty lim (\frac{4}{x ^{2}})

\frac{d y}{d x} = e^{y}

What is (\partial)/(\partial x)(ln(3x+6y+9z)) ?
The answer to (\partial)/(\partial x)(ln(3x+6y+9z)) is 1/(x+2y+3z)