Examples and practice
Techniques of differentiation
Back to lessonPractice section 1 · Questions 1–6
Evaluate finite and infinite limits in two ways · Derive the derivative of a square from first principles · +4 more
Practice section 2 · Questions 7–12
Practise power, chain and product rules together · Choose useful trig identities before differentiating · +4 more
- Practise power, chain and product rules together
- Choose useful trig identities before differentiating
- Prove a cotangent derivative and distinguish a reciprocal from an inverse
- Prove a squared-cosine derivative identity
- Differentiate exponentials and logarithms with their inner factors
- Simplify a logarithm before differentiating
Practice section 3 · Questions 13–18
Practise products, exponentials and a logarithmic square root · Collect the derivative terms in implicit relations · +4 more
Practice section 4 · Questions 19–24
Combine a square root with inverse cosine · Evaluate a derivative at a point with the source calculator workflow · +4 more
- Combine a square root with inverse cosine
- Evaluate a derivative at a point with the source calculator workflow
- Prove the reciprocal derivative from first principles
- Use first principles and the sine small-angle limit
- Derive the exponential derivative using its limiting quotient
- Prove the inverse-cosine derivative using its principal range
Practice section 5 · Questions 25–30
Prove the inverse-tangent derivative by implicit differentiation · A nested derivative, correct to five significant figures · +4 more
- Prove the inverse-tangent derivative by implicit differentiation
- A nested derivative, correct to five significant figures
- Nine derivatives: chain, product, quotient and inverse functions
- Implicit differentiation with an exponential
- Implicit differentiation involving inverse sine
- A variable base and exponent
Practice section 6 · Questions 31–36
An inverse sine derivative with two branches · Single-fraction derivatives and an implicit slope · +4 more
- An inverse sine derivative with two branches
- Single-fraction derivatives and an implicit slope
- Three chain-rule derivatives
- Differentiate an inverse tangent and a logarithmic square root
- Differentiate a square root of inverse cosine and a logarithmic radical
- Give single-fraction derivatives of a log radical and inverse tangent
Practice section 7 · Questions 37–42
Use chain, logarithmic, product and quotient differentiation · Differentiate a product with constant-e exponent and a variable power · +4 more
- Use chain, logarithmic, product and quotient differentiation
- Differentiate a product with constant-e exponent and a variable power
- Use a stated interval to choose the square-root sign
- Differentiate an exponential of a trigonometric function implicitly
- Collect implicit derivative terms with a constant-base exponential
- Take logarithms of a positive variable power
Practice section 8 · Questions 43–45
Logarithmically differentiate an implicit variable power · Compare direct and logarithmic implicit differentiation · +1 more