Question

Find the derivative of sin(2x + 3y)= 3xy + 5y-2.

I have this so far

1) cos(2x+3y) * d/dx (2x+3y)= 3xy' + 3y + 5y'

2) cos (2x+3y) * [2 + 3y']= 3xy' + 3y + 5y'

3) 3y' cos (2x+3y) + 2cos(2x+3y)= 3xy' + 3y + 5y'

4) 3xy' + 5y' - (3y(cos(3x+3y)= 2 cos (2x + 3y) - 3y

If I am wrong, can you please explain to me what I am doing wrong. Thank you

Answer 1

Aside from the typos in (4) you are ok.

4) 3xy' + 5y' - 3cos(2x+3y)y' = 2 cos (2x + 3y) - 3y

5) (3x+5y-3cos(2x+3y))y' = 2cos(2x+3y) - 3y

6) y' = (2cos(2x+3y)-3y)/(3x+5y-3cos(2x+3y))

Answer 2

Thank you SO much sir. I feel a lot better knowing that I did this right