Apply Differentiation Rules (HSC SSCE Mathematics Advanced): Quizzes

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Apply Differentiation Rules
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What is the chain rule formula for y=f(g(x))y = f(g(x)) where u=g(x)u = g(x)?

dydx=dydu×dudx\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}

When should you apply the product rule?

When two functions are multiplied

What is the quotient rule formula for y=u(x)v(x)y = \frac{u(x)}{v(x)}?

vdudxudvdxv2\frac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^2}

Which rule is needed for (3x5)4(3x - 5)^4?

Chain rule

What's the memory aid for the product rule?

First × deriv. of 2nd + 2nd × deriv. of 1st

What pattern describes the quotient rule?

Bottom × top' - top × bottom', over bottom²

How does the chain rule work with composite functions?

From outside in

What should you identify first when differentiating complex functions?

The outermost operation

For y=x2+92x3+1y = \sqrt{\frac{x^2 + 9}{2x^3 + 1}}, what is the gradient at x=0x = 0?

00

For f(x)=2x(x+8)(4x2)f(x) = 2\sqrt{x}(x + 8)(4 - x^2), what is the tangent line equation at x=1x = 1?

y=3x+57y = -3x + 57

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