What is (\partial)/(\partial t)(ln(3x+3ct)) ?

The answer to (\partial)/(\partial t)(ln(3x+3ct)) is c/(x+ct)

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(\partial)/(\partial t)(ln(3x+3ct))

\frac{\partial}{\partial t} (ln (3 x + 3 c t))

\frac{c}{x + c t}

Solution steps

\frac{\partial}{\partial t} (ln (3 x + 3 c t))

Treat

c, x

as a constant

Apply the chain rule:

\frac{1}{3 x + 3 c t} \frac{\partial}{\partial t} (3 x + 3 c t)

= \frac{1}{3 x + 3 c t} \frac{\partial}{\partial t} (3 x + 3 c t)

\frac{\partial}{\partial t} (3 x + 3 c t) = 3 c

= \frac{1}{3 x + 3 c t} \cdot 3 c

Simplify

\frac{1}{3 x + 3 c t} \cdot 3 c : \frac{c}{x + c t}

= \frac{c}{x + c t}

x \to 0 lim (\frac{1}{x} - \frac{1}{e ^{x}})

\frac{1}{( s ^{2} + 1 ) ( s ^{2} + 16 )}

x \to 2 lim (x^{2} - 4 x + 5)

\frac{d}{d x} (- \frac{2 x}{( x ^{2} - 1 ) ^{2}})

\int 21 x^{3} e^{x} d x

What is (\partial)/(\partial t)(ln(3x+3ct)) ?
The answer to (\partial)/(\partial t)(ln(3x+3ct)) is c/(x+ct)