Question

Differentiate the function. f(x) = ln(25 sin^2(x))

Answer 1

Use the chain rule.
Let u = 25sin²(x), such that dy/dx = dy/du · du/dx


`(dy)/(dx) = (1)/(25sin^(2)(x)) \cdot 50cos(x) \cdot sin(x)`

`(dy)/(dx) = (2cos(x) sin(x))/(sin^(2)(x))`


`(dy)/(dx) = 2cot(x)`