What is (\partial)/(\partial t)(ln(kx-mt)) ?

The answer to (\partial)/(\partial t)(ln(kx-mt)) is -m/(kx-mt)

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(\partial)/(\partial t)(ln(kx-mt))

\frac{\partial}{\partial t} (ln (k x - m t))

- \frac{m}{k x - m t}

Solution steps

\frac{\partial}{\partial t} (ln (k x - m t))

Treat

k, x, m

as constants

Apply the chain rule:

\frac{1}{k x - m t} \frac{\partial}{\partial t} (k x - m t)

= \frac{1}{k x - m t} \frac{\partial}{\partial t} (k x - m t)

\frac{\partial}{\partial t} (k x - m t) = - m

= \frac{1}{k x - m t} (- m)

Simplify

\frac{1}{k x - m t} (- m) : - \frac{m}{k x - m t}

= - \frac{m}{k x - m t}

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

\frac{d}{d x} (\frac{4 x}{9 y})

\frac{d}{d x} (- 7 (3 x^{4} + 2)^{- 4})

\frac{d}{d x} (\frac{2}{x ^{2} + 5})

x \to 5 lim (\frac{x + 1}{x - 5})

What is (\partial)/(\partial t)(ln(kx-mt)) ?
The answer to (\partial)/(\partial t)(ln(kx-mt)) is -m/(kx-mt)