The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Derivatives, chain rule and domains
Differentiate rational powers, sums and simplified expressions.
Use the chain rule with linear and nonlinear inner functions.
Connect a chord gradient to an instantaneous gradient; retain domains.
Write roots and reciprocals as powers. Use \(\displaystyle \frac{d}{dx}x^n=nx^{n-1}\) and \(\displaystyle \frac{d}{dx}[u(x)]^n=n[u(x)]^{n-1}u^{\prime}(x)\). Expand or simplify products and quotients first. A derivative is a gradient, not a coordinate; check where it is finite.