Question

First derivative of sqrt(2(3^x)) × log(2x+5)

Answer 1

Your two questions about derivation are very difficult to explain on this site.

Therefore in google paste:

emathhelp derivative calculator

When you see the list of results click on:

Online Derivative Calculator with Steps - eMathHelp

When the page be open in the rectangle Function paste your function.

Then click the option CALCULATE

You will see a step-by-step solution.


And one more explanation:

( 5 x - 2 ) ⁻ ³ = 1 / ( 5 x - 2 ) ³

Of course:

- 2 + 3 x = 3 x - 2

- 2 + 5 x = 5 x - 2

Answer 2

y = √(2(3^x)) * log(2x+5) = √2 3^(x/2) log(2x+5)
use the product rule to get
y' = √2 [ 3^(x/2) * (1/2) log3 log(2x+5) + 3^(x/2) * 1/(2x+5) * 2)]