Question

How do you differentiate `g(x) = sqrt(x-1)cos(7x)` using the product rule?

Answer 1

`f=(x-1)^(1/2), g=cos(7x)->f'=1/(2sqrt(x-1)),g' = -7sin(7x)`
`g'(x)=fg'+gf'=-7sqrt(x-1)sin(7x)+cos(7x)/(2sqrt(x-1))`

Explanation:

Separate the product into f and g and find f' and g' then put it into the product rule