What is (\partial)/(\partial t)(ln(x+2ct)) ?

The answer to (\partial)/(\partial t)(ln(x+2ct)) is (2c)/(x+2ct)

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(\partial)/(\partial t)(ln(x+2ct))

\frac{\partial}{\partial t} (ln (x + 2 c t))

\frac{2 c}{x + 2 c t}

Solution steps

\frac{\partial}{\partial t} (ln (x + 2 c t))

Treat

c, x

as a constant

Apply the chain rule:

\frac{1}{x + 2 c t} \frac{\partial}{\partial t} (x + 2 c t)

= \frac{1}{x + 2 c t} \frac{\partial}{\partial t} (x + 2 c t)

\frac{\partial}{\partial t} (x + 2 c t) = 2 c

= \frac{1}{x + 2 c t} \cdot 2 c

Simplify

\frac{1}{x + 2 c t} \cdot 2 c : \frac{2 c}{x + 2 c t}

= \frac{2 c}{x + 2 c t}

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\int (cos (x) sin^{2} (x)) d x

\frac{d}{d x} (\frac{2 x ^{2} - 1}{x ^{2} - 3})

\int 20 x^{3} + 12 x^{2} + 4 d x

What is (\partial)/(\partial t)(ln(x+2ct)) ?
The answer to (\partial)/(\partial t)(ln(x+2ct)) is (2c)/(x+2ct)