Question

Find Devivaties with respect to x:

1). y=sin(cos(x+3));

2). tan(x+y)=ln x+ 5y.

Answer 1

Hints:
1. apply the chain rule "twice" (the third time, the derivative of x+3 is just 1): f(g(x+3))'=f'(g(x+3))*g'(x+3)*1
2. I don't know if there's a nice trig identity to help you split up the x and y in tan(x+y), but even if there is, it is likely that you will have to use implicit differentiation.