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

The answer to (\partial ^2)/(\partial x^2)(ln(3x+3ct)) is -1/((x+ct)^2)

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

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

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

Solution steps

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

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

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

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

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

\int_{0}^{1} \frac{40}{x ^{2} - 100} d x

2^{x}, (0, 2)

x \to 8 lim (x^{2} - 9)

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

x^{19} e^{x}

What is (\partial ^2)/(\partial x^2)(ln(3x+3ct)) ?
The answer to (\partial ^2)/(\partial x^2)(ln(3x+3ct)) is -1/((x+ct)^2)