What is the second derivative of f(x)= ln sqrt(3x-7)?

1 Answer

Hence the function can be written as follows

f(x)= ln sqrt(3x-7)=>f(x)=ln(3x-7)^(1/2)=> f(x)=1/2*ln(3x-7)

The first derivative is

$\frac{\mathrm{df}}{\mathrm{dx}} = \frac{1}{2} \cdot \frac{\left(3 x - 7\right) '}{3 x - 7} = \frac{1}{2} \cdot \frac{3}{3 x - 7}$

Finally

$f ' \left(x\right) = \frac{3}{2 \cdot \left(3 x - 7\right)}$