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

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

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

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

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

Solution steps

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

Treat

y, t

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

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

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