Differentiate f(x)=sin(x)+7/9cot(x)

Question

Would the Sum rule be used so the answer cos(x)-csc^2(x)

Answer 1

Yes, you can use the Sum rule.

However, don't forget the 7/9 coefficient.

f'(x) = cos(x) - (7/9)csc²(x)

If f(x) = sin(x) + 7/(9cot(x)) that's a different problem.

f(x) = sin(x) + (7/9)tanx(x)

f'(x) = cos(x) + (7/9)sec²(x)