Find the Derivative
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\( f(x) = ... \)
\( f'(x) = \)
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Derivative Rules
- Power Rule: \( \frac{d}{dx}(x^n) = nx^{n-1} \)
- Chain Rule: \( \frac{d}{dx}(f(g(x))) = f'(g(x))g'(x) \)
- Sine Rule: \( \frac{d}{dx}(\sin(u)) = \cos(u) \cdot u' \)
- Cosine Rule: \( \frac{d}{dx}(\cos(u)) = -\sin(u) \cdot u' \)
- Natural Log: \( \frac{d}{dx}(\ln(u)) = \frac{1}{u} \cdot u' \)
- Square Root: \( \frac{d}{dx}(\sqrt{u}) = \frac{1}{2\sqrt{u}} \cdot u' \)
- Arcsin: \( \frac{d}{dx}(\arcsin(u)) = \frac{u'}{\sqrt{1-u^2}} \)
- Arctan: \( \frac{d}{dx}(\arctan(u)) = \frac{u'}{1+u^2} \)