Introduction to using the product rule

Given cost of production and price of sale of a product; a percentage increase in cost of production; and unit sales before and after; work out the extra profit.

Based on question 6 from section 3 of the maths-aid workbook on numerical reasoning.

Using the chain rule within product rule problems

Introduction to using the product rule

Introduction to using the product rule

Using the chain rule within product rule problems

Oefeningen:

BASIS: Maak een extra "part" aan, waar om het product van de twee breuken gevraagd wordt.

BASIS: Zoek uit waar typische_fout voor dient (bij de variabelen) en hoe die typische fout dan effectief gesignaleerd wordt.

GEMIDDELD: Zorg dat geen/enkel (jouw keuze) noemers voorkomen die geen gemeenschappelijke deler hebben. (Hint: gcd(a,b) kan een hulp zijn, met een for-loop.)

Simplify (a) a fully-factorised fraction with common factors, and (b) a fraction where the numerator is a product and the denominator a sum sharing the same variables (that cannot be simplified). The variables are randomised. Part of HELM book 1.4

Simplify a fraction where the numerator and denominator are factorised and have common products, and one of the common factors is powered. Part of HELM book 1.4

Differentiate $f(x) = x^m(a x+b)^n$.

Finding the product of a linear function of the form $mx+c$ and a cubic function of the form $ax^3+bx^2+cx+d$.

Finding the product of two linear functions of the form $mx+c$ and a quadratic function of the form $ax^2+bx+c$.

Finding the product of three linear functions of the form $mx+c$.

Finding the product of two linear functions of the form $mx+c$.

Calculate the product of two quadratic expressions of the form $ax^2+bx+c$.

Factorise a cubic expression into the product of three linear factors of the form $mx+c$, where one of the factors is given. 

Calculate the product of two randomised scientific notation numbers and give the answer in scientific notation.

Part of HELM Book 1.2

Students are given three expanded products and asked to write them in index notation. Part of HELM Book 1.2

Introduction to using the product rule

Using some passages of text, fill in a product fact sheet.

A simple example showing how to mark entries in a spreadsheet.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

Use the product rule (number of ways of doing A and B = (no. for A)*(no. for B)) to count the number of ways of doing two independent tasks.

Students are asked to find either the initial production cost, or a gradient, or the break even point from a graph.
They are then asked to determine the profit or loss from the graph for the production of a particular number of units. This number is randomised.

Given the vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, calculate $(\mathbf a \times \mathbf b) \times \mathbf c$ and $\mathbf a \times (\mathbf b \times \mathbf c)$.

Find a perpendicular vector to a pair of vectors.