Logarithmic Differentiation – Solved Example (2)

Take natural logarithm on both sides and simplify by the help of logarithm laws:

Differentiate both sides of the equation completely:

Applying chain rule, substitute u = f(x), v = sin x + 1, w = cos x – 1 and s = sin x – 1,

Cross multiply f(x) from left hand side denominator to the right hand side of the equation and substitute the original expression for f(x):