What is (\partial)/(\partial x)(ln(x+4y+9z)) ?

The answer to (\partial)/(\partial x)(ln(x+4y+9z)) is 1/(x+4y+9z)

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(\partial)/(\partial x)(ln(x+4y+9z))

\frac{\partial}{\partial x} (ln (x + 4 y + 9 z))

\frac{1}{x + 4 y + 9 z}

Solution steps

\frac{\partial}{\partial x} (ln (x + 4 y + 9 z))

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{x + 4 y + 9 z} \frac{\partial}{\partial x} (x + 4 y + 9 z)

= \frac{1}{x + 4 y + 9 z} \frac{\partial}{\partial x} (x + 4 y + 9 z)

\frac{\partial}{\partial x} (x + 4 y + 9 z) = 1

= \frac{1}{x + 4 y + 9 z} \cdot 1

Simplify

= \frac{1}{x + 4 y + 9 z}

y = 6 x - x^{2}, (1, 5)

\int \frac{x + 2}{x ^{2} + 9} d x

\int \frac{6}{x - 5} d x

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

\int_{0}^{12} 1 + \frac{x}{4} d x

What is (\partial)/(\partial x)(ln(x+4y+9z)) ?
The answer to (\partial)/(\partial x)(ln(x+4y+9z)) is 1/(x+4y+9z)