Differentiate the following ( do not simplify)

Question

a) ln(√sinx)

Answer 1

Use the chain rule:
d(ln(√sin(x)))/dx
=[1/(√sin(x))]*d√(sin(x))/dx
=[1/(√sin(x))]*[1/(2√(sin(x)))]*d(sin(x))/dx
=[1/(√sin(x))]*[1/(2√(sin(x)))]*cos(x)