The Reverse Chain Rule (HSC SSCE Mathematics Advanced): Flashcards

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The Reverse Chain Rule
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Purpose of reverse chain rule

Find primitives from chain rule differentiation

Reverse chain rule: undudxdx\int u^n \frac{du}{dx} dx

un+1n+1+C\frac{u^{n+1}}{n+1} + C

Reverse chain rule: (f(x))nf(x)dx\int (f(x))^n f'(x) dx

(f(x))n+1n+1+C\frac{(f(x))^{n+1}}{n+1} + C

Pattern in reverse chain rule integrand

Derivative × power of inner function

Key identification in reverse chain rule

Inner function and its derivative in integrand

Technique to match derivative in reverse chain rule

Factor out constants

When to add constant C in integration

Only in final answer

Do both reverse chain rule formulas give same result?

Yes, identical results

What to check with definite integrals

The domain

Required form of integrand for reverse chain rule

Product of two factors

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