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21-04-2017
Mathematics

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

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21-04-2017

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

[tex]\frac{dy}{dx} = \frac{1}{25sin^{2}(x)} \cdot 50cos(x) \cdot sin(x)[/tex]
[tex]\frac{dy}{dx} = \frac{2cos(x) sin(x)}{sin^{2}(x)}[/tex]

[tex]\frac{dy}{dx} = 2cot(x)[/tex]

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