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

Answer 1

Ezekiel Alexander

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

#(df)/dx=1/2*((3x-7)')/(3x-7)=1/2*3/[3x-7]#

Finally

#f'(x)=3/(2*(3x-7))#

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Answer 2

Charles Arocha

To find the second derivative of ( f(x) = \ln(\sqrt{3x - 7}) ), we first find the first derivative and then differentiate it again.

First, let's find the first derivative using the chain rule:

[ f'(x) = \frac{1}{\sqrt{3x - 7}} \cdot \frac{1}{2\sqrt{3x - 7}} \cdot 3 ]

[ f'(x) = \frac{3}{2(3x - 7)} ]

Now, let's differentiate ( f'(x) ) to find the second derivative:

[ f''(x) = \frac{d}{dx}\left(\frac{3}{2(3x - 7)}\right) ]

[ f''(x) = \frac{-3}{2(3x - 7)^2} \cdot 3 ]

[ f''(x) = \frac{-9}{2(3x - 7)^2} ]

So, the second derivative of ( f(x) = \ln(\sqrt{3x - 7}) ) is ( \frac{-9}{2(3x - 7)^2} ).

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Answer from HIX Tutor

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