Differentiating y = e²ˣ·ln(x² + 1)

Calculus 1 · Axiom Academy

EXAMPLE Differentiating a Complex Product Combine the product rule with the chain rule to differentiate a product of two functions. Find the derivative of . This is a product of two functions, and each factor needs the chain rule before we can put the product rule together. Nice work. You differentiated a product whose factors each needed the chain rule. Here is what to carry forward: Product rule: for f(x)g(x) , use (fg)' = f'g + fg' . Chain rule for exponentials: , so . Chain rule for logarithms: , so . Complex derivatives often stack several rules — name each factor, differentiate it on its own, then assemble.

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