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Find the derivative of $ \sin(x^2) $ with respect to $ x $

Answer 1 To find the derivative of $ \sin(x^2) $ with respect to $ x $, we use the chain rule: $$ \frac{d}{dx} \sin(u) = \cos(u) \cdot \frac{du}{dx} $$ Here, let $ u = x^2 $. Then: $$ \frac{du}{dx} = \frac{d}{dx}(x^2) = 2x $$ Now apply the chain...