Question

find the derivative of 5sinx/2+cosx...... what happens to the 5 when taking the d of sin? does it stay in front of the whole thing?

Answer 1

and does sinx*cosx turn into 1?

Answer 2

yes.
no.

Answer 3

The 5 "stays out front" because when you do the product rule, the derivative of 5 is 0, so you lose that term and just have the term with 5 and the derivative of sine.

for example,
d/dx 2sinx = 0*sinx+2cosx=2cosx