Are these answers okay??

Question

I hope I'm not being annoying, but seeing as I'm not too confident with differential calculus I'd like to know if my solutions to the following are okay.

Q: Differentiate with respect to x:

a) g(x) = 1 -1/x

= 1/x^2 ?

b) h(x) = 2e^x

= 2e^x Log(e) ?

c) j(x) = sin(x) + cos(x)

= cos(x) - sin(x) ?

d) k(x) = ln (x)

= 1/x ?

Answer 1

a) is correct.

b) is incorrect since e^x = exp(x) and d/dx (expx) = expx, hence, the answer should be:

2exp(x)

c) is correct; d) is correct

Answer 2

b) h(x) = 2e^x ==> h'(x) = 2e^x