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List of top Mathematics Questions on Derivatives

If $ y = \frac{b}{a} $, then $ \frac{dy}{dx} $ is:
If \( y = x^x + x^x \), then find \( \frac{dy}{dx} \):
Given \( f'(1) = 3 \), \( f(1) = 1 \), and
\[ y = f\left(f(f(x))\right) + \left(f(x)\right)^2, \] then find \( \frac{dy}{dx} \) at \( x = 1 \).
If \( y = \log_e \left[ e^{3x} \left( \frac{x - 4}{x + 3} \right)^{3/2} \right] \), then find \( \frac{dy}{dx} \):