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

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

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

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

\frac{1}{x + 6 y + 9 z}

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

\int_{0}^{\frac{π}{2}} tan (\frac{x}{2}) d x

25 y^{^{''}} - 40 y^{^{'}} + 16 y = 0, y (0) = 4, y^{^{'}} (0) = - 5

\int ln (x^{\frac{1}{2}}) d x

\frac{s}{( s - 1 ) ^{2}}

\frac{\partial}{\partial x} (e^{e^{x}})

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