Here are a couple of sin cos differentiation questions. My teacher has gone over the rules for a bit but hasn't shown how to do the actual equation questions.
we find dy/dx using the product rule and the quotient rule:
dy/dx = d/dx[x/(1+e^x)] cos(x) + [x/(1+e^x)] d/dx cos(x)
Now you need to use the quotient rule to do the first of the derivatives on
the right above. Me I don't know the quotient rule so I will use the product
rule a second time:
d/dx[x/(1+e^x)] = 1/(1+e^x) - x e^x /(1+e^x)^2 = (1 - e^x (x - 1))/(e^x + 1)^2
dy/dx = [(1 - e^x (x - 1))/(e^x + 1)^2] cos(x) - [x/(1+e^x)] sin(x)