2 interactive labs · AS & A Level Mathematics 9709
Chain, Product and Quotient Rules
3.4 Differentiation (also 2.4) · Choose the rule (chain, product, quotient or a combination), expose u, v, u′ and v′, build dy/dx, then check it against a measured tangent gradient.
Loading simulation…
About this lab
Choose the rule (chain, product, quotient or a combination), expose u, v, u′ and v′, build dy/dx, then check it against a measured tangent gradient.
You will be able to
Determine from the outermost operation whether a function needs the chain rule, the product rule, the quotient rule or a combination of two.
Differentiate products, quotients and composites of eˣ, ln x, sin x, cos x and tan x, writing u, v, u′ and v′ before assembling dy/dx.
Deduce the value of dy/dx at a point and verify it against the measured gradient of the tangent.
Explain why the derivative of a product is not the product of the derivatives, and why the order of the quotient rule's numerator matters.
Parametric and Implicit Curves: Tangent and Normal
3.4 Differentiation (also 2.4) · Walk along x = t − e^(2t), y = t + e^(2t) and x² + y² = xy + 7: predict dy/dx, then see the tangent, the normal and where dy/dx is undefined.
Loading simulation…
About this lab
Walk along x = t − e^(2t), y = t + e^(2t) and x² + y² = xy + 7: predict dy/dx, then see the tangent, the normal and where dy/dx is undefined.
You will be able to
Calculate dy/dx for a parametric curve as (dy/dt) ÷ (dx/dt), and for an implicit curve by differentiating every term with respect to x.
Find the equations of the tangent and the normal at a given point of a parametric or an implicit curve.
Determine where dy/dx is not defined (a vertical tangent, a zero denominator) and where it is 0 (a horizontal tangent).
Explain why dy/dx for an implicit curve depends on both x and y, so that one value of x can have two different gradients.
