Question

Differentiate f(x) = ln(x)/sin(x)

Answer 1

Possible derivation:
d/dx(f(x)) = d/dx(log(x) csc(x))

The derivative of f(x) is f'(x):
f'(x) = d/dx(log(x) csc(x))

Use the product rule, d/dx(u v) = v ( du)/( dx)+u ( dv)/( dx), where u =csc(x) and v = log(x):
f'(x) = log(x) (d/dx(csc(x)))+csc(x) (d/dx(log(x)))

The derivative of log(x) is 1/x:
f'(x) = log(x) (d/dx(csc(x)))+(csc(x))/x

The derivative of csc(x) is -cot(x) csc(x):

Answer
| f'(x) = (csc(x))/x+log(x) (-(cot(x) csc(x)))