5. Differentiation

5.01 The power rule

5.02 The chain rule

5.03 The product rule

5.04 The quotient rule

INVESTIGATION: Exponential functions

5.05 Differentiation and exponential functions

INVESTIGATION: Limits and trigonometric functions

5.06 Differentiation and trigonometric functions

5.07 Further differentiation

5.08 Newton's method

5.09 Differentiation and logarithms

VCE 12 Methods 2023

5.01 The power rule

Interactive practice questions

Differentiate $y=3x^2$y=3x2

Easy

< 1min

Determine the derivative of $y=x^2-x+8$y=x2−x+8.

Easy

< 1min

Determine the derivative of $y=\frac{-2}{x^5}$y=−2x5.

Easy

1min

Differentiate $y=7x^{-3}$y=7x−3.

Easy

< 1min

Outcomes

U34.AoS3.2

derivatives of 𝑥^n, e^x, log_e(x), sin (𝑥), cos(𝑥) and tan (𝑥)

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

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