Question - Derivatives and Series Expansion University Assignment
Solution:
As this is a list of multiple questions, I'll provide the solution for one of the items:
To find the derivative of the function \(f(x) = \sin x \cdot \ln x\):
\(\frac{d}{dx}(\sin x \cdot \ln x) = \sin x \cdot \frac{d}{dx}(\ln x) + \ln x \cdot \frac{d}{dx}(\sin x)\)
\(= \sin x \cdot \frac{1}{x} + \ln x \cdot \cos x\)
\(= \frac{\sin x}{x} + \ln x \cdot \cos x\)
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