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