Ask Me Help Desk - Logarithmic & Exponential Derivatives (Cal-1)

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Logarithmic & Exponential Derivatives (Cal-1)

Hi.
I'm in CEGEP and am currently in Calculus 1.
I am having a great deal of difficulty with logarithimic and exponential derivatives such as the questions that are attached.
In all cases, the questions are asking for the first derivative.
Any detailed workings would be greatly appreciated.
Thanks!

Attachment 5159

Attachment 5160

Attachment 5161

For the first one, rewrite as:

$\frac{1}{2}\left[ln(6x-5)-ln(3x+7)\right]$

For the 2nd one, rewrite as:

$9ln(x)+2ln(x+4)+8ln(x^{2}+2)$

For the 3rd, can you use the product rule? That's about all it is.

$5\sqrt{x}ln(x)$

product rule:

$5(\sqrt{x}\cdot\frac{1}{x}+ln(x)\cdot\frac{1}{2sqr t{(x)}})$

Now simplify.

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