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}

\frac{d x}{d t} + \frac{3 x}{500} = 0.6

f (x) = \frac{1}{1 + 5 x ^{2}}, at x = - 1

\int x^{2} (sin (π x)) d x

\frac{d}{d t} (7 t)

\frac{\partial}{\partial x} (\frac{x}{y} - sin (y))

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