# differentiation basics

► syllabus content for the Calculus Topic: SL syllabus (see syllabus section 6.1 ); HL syllabus (see syllabus section 6.1).

The introductory content for differential calculus is not too different between Maths HL and Maths SL. In both courses students need to understand the limit definition of the derivative (first principles) and to be able to use it to find the derivative of some simple functions.

Although I prefer an emphasis on concepts - such as rates of change, limits of functions, relationship between slope (gradient) of a secant line and slope of a tangent line, slope of a curve at a point, etc - I also think it's important that students become fluent and confident with the rules of differentiation.

I've written some detailed notes on differentiation basics where you find here on another page.

Also have a look at my Geogebra applet secant-tangent-derivative where you can dynamically change the gradient of a secant line to approximate the gradient of a line tangent to a curve at a point.

### 4 questions - ‘accessible’ to ‘discriminating’

accessible SL question

moderate SL / accessible HL question

discriminating SL / moderate HL question

discriminating HL question

#### ♦ teaching materials

EXS_6-1-15v1_SLHL_differentiation_1
Differentiation Practice-1:  Exercise set with 7 questions.  Syllabus content covered is listed at start.  No GDC allowed.  Worked solutions are included. This exercise set is the 1st in a set of 3 intended to give students practice in many of the basic techniques and applications of differential calculus.

EXS_6-1-25v2_SLHL_differentiation_2
Differentiation Practice-2: topics covered include differentiation of polynomials; chain rule; quotient rule; identifying and verifying stationary points inflexion points; finding lines tangent and/or normal to a curve.  Worked Solutions included

EXS_6-1-35v1_SLHL_differentiation_3
Differentiation Practice-3:  Exercise set with 15 questions (answers included).  No GDC allowed.  This exercise set is the 3rd in a set of 4 intended to give students practice in many of the basic techniques and applications of differential calculus.

EXS_6-1-45v1_SLHL_differentiation_4
Differentiation Practice-4: Exercise set with 13 questions. No GDC, except on three of the questions. This is the 4th and last exercise set for covering many of the basic techniques & applications of differential calculus. Worked solutions available below.

EXS_6-1-45v1_SLHL_differentiation_4_SOL_KEY
Worked solutions for the Differentiation-4 exercise set above.

Quiz_SLHL_diff_rules_v1
Short quiz (SL: 3 questions; HL: 4 questions) with questions on finding a tangent, normal, max & min points that require use of the differentiation rules: chain rule, product rule & quotient rule. Q.4 is for HL only. Worked solutions available below.

Quiz_SLHL_diff_rules_v1_SOL_KEY
Worked solutions for quiz on differentiation rules above.

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