Topics
5. Differentiation
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AustraliaVIC
VCE 12 Methods 2023

5.07 Further differentiation

Lesson
Worksheet
Practice

Interactive practice questions

Differentiate $y=x^7+3x^4+\sqrt[3]{x+4}$y=x7+3x4+3√x+4.

Easy
1min

Differentiate $y=\left(x+7\right)^5-\frac{3}{x^4}$y=(x+7)5−3x4​.

Easy
2min

Differentiate $y=4x^5+\frac{1}{x-4}+6$y=4x5+1x−4​+6.

Express the answer in positive index form.

Easy
2min

Differentiate $y=\frac{3}{x+7}+\frac{6x+7}{3}$y=3x+7​+6x+73​.

Easy
2min
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Outcomes

U34.AoS3.3

derivatives of f(x) +/- g(x), f(x) x g(x), f(x)/g(x) and (𝑓 ∘ 𝑔)(𝑥) where f and g are polynomial functions, exponential, circular, logarithmic or power functions and transformations or simple combinations of these functions

U34.AoS3.17

apply the product, chain and quotient rules for differentiation to simple combinations of functions by hand

U34.AoS3.16

find derivatives of polynomial functions and power functions, functions of the form f(ax+b) where f is x^n, sine, cosine; tangent, e^x, or log x base e and simple linear combinations of these, using pattern recognition, or by hand

U34.AoS3.18

find derivatives of basic and more complicated functions and apply differentiation to curve sketching and optimisation problems

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