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

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The Reverse Chain Rule
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What does the chain rule produce when differentiating a composite function?

A product of two terms

What does the reverse chain rule allow us to find?

Primitives (antiderivatives)

When should you add the arbitrary constant CC in integration?

Only in the last line

What is ∫undudxdx\int u^n \frac{du}{dx} dx equal to?

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

What is the key challenge when using the reverse chain rule formula?

Identifying which part is uu or f(x)f(x)

What is ∫12x2(x3+5)3dx\int 12x^2(x^3 + 5)^3 dx equal to?

(x3+5)4+C(x^3 + 5)^4 + C

What is the crucial insight for ∫x2(x3+5)3dx\int x^2(x^3 + 5)^3 dx?

x2x^2 is a multiple of ddx(x3+5)\frac{d}{dx}(x^3+5)

How is 1−x2\sqrt{1 - x^2} rewritten as a power?

(1−x2)12(1 - x^2)^{\frac{1}{2}}

What pattern should you look for in the reverse chain rule?

(derivative) × (power of inner function)

What must always be checked when evaluating definite integrals?

The domain

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