f(x) = (sin(x) - 1) * (3x + cos(x-5))

Question

before using differentiation, do I have to FOIL the problem first? i need help.

Answer 1

You don't have to.

 

You can use the product rule to find the derivative based on the derivatives of the two terms in parentheses:

 

D_x (sin(x) - 1) * (3x + cos(x-5)) =

(sin(x) - 1) D_x (3x + cos(x-5)) + (3x + cos(x-5)) D_x (sin(x) - 1) =

(sin(x) - 1) (3 - sin (x-5)) + (3x + cos(x-5)) cos x

 

Now multiply all the terms out, and see what you end up with.