What is (\partial ^2)/(\partial t^2)(ln(3x+3ct)) ?

The answer to (\partial ^2)/(\partial t^2)(ln(3x+3ct)) is -(c^2)/((x+ct)^2)

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(\partial ^2)/(\partial t^2)(ln(3x+3ct))

\frac{\partial ^{2}}{\partial t ^{2}} (ln (3 x + 3 c t))

- \frac{c ^{2}}{( x + c t ) ^{2}}

Solution steps

\frac{\partial ^{2}}{\partial t ^{2}} (ln (3 x + 3 c t))

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

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

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

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

e^{y} y^{^{'}} = \frac{sin ( x )}{cos ^{2} ( x )}

\frac{d}{d x} (e^{s i n (x^{2})})

y^{^{'}} - 7 y = sin (2 x)

y = 1 + x - 4 x^{\frac{1}{2}}

arctan (\frac{1 + x}{1 - x})

What is (\partial ^2)/(\partial t^2)(ln(3x+3ct)) ?
The answer to (\partial ^2)/(\partial t^2)(ln(3x+3ct)) is -(c^2)/((x+ct)^2)