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

$\frac{dy}{dx} = \frac{1}{25sin^{2}(x)} \cdot 50cos(x) \cdot sin(x)$
$\frac{dy}{dx} = \frac{2cos(x) sin(x)}{sin^{2}(x)}$

$\frac{dy}{dx} = 2cot(x)$