3.4.3—Differentiation rules

Power, exponential, logarithmic, trigonometric, product, quotient and chain rules are building blocks; a single expression may require several in sequence.

Rewrite constants and nested powers, mark the outermost operation, and check a derivative numerically at one simple point if the algebra is long.

For y=(x²+1)^2e^x, use product plus chain: y′=e^x[(x²+1)^2+4x(x²+1)].

A familiar-looking power does not override a product or composite structure; missing one rule changes the result.