MATHS HOLIDAY HOMEWORK DIFFERENTIATION

…contents… Introduction Basic Formulas Of Differentiation Product Rule Quotient Rule Examples Chain Rule Trigonometric Functions Use Of Differentiation Click on topics to go on desired slide

…Introduction… B = = a = intercept Differentiation is all about measuring change! Measuring change in a linear function: y = a + bx a = intercept b = constant slope i.e. the impact of a unit change in x on the level of y B = =

Derivative = Slope of Tangent Line

…Basic Differentiation Rules… 1. Ex 2. Ex

…Contd… 3. Ex. 4. Ex.

…Product rule… In words, the derivative of a product of two functions is the first function times the derivative of the second plus the second function times of the first.

…quotient rule… In words, the derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by denominator squared.

…examples… Product Rule Quotient Rule

…chain rule… EG - The derivative of f(g(x)) is the derivative of the outside function evaluated at the inside function times the derivatives of inside function.

…trigonometric function…

…use of differentiation in real life… Differentiation is very important in many fields, and has made great contributions in these fields, which are still noticed nowadays. The differentiation of calculus have many real- world applications from sports to engineering to astronomy to math and space travel.

…uses in economics and science… Functions and derivatives of calculus are relate to relevant concepts in economics. Economic research uses calculus functional relationships, relation of income , market prediction etc  Isaac Newton developed the use of calculus in his laws of motion and gravitation. Astronomical science deeply depend on calculus. Calculus is used to build tracks.

…in engineering and biology… Calculus initially developed for better navigation system. Engineers use calculus for building skyscrapers , bridges. In robotics calculus is used how robotic parts will work on given command. Calculus is used for measuring growth rate of bacteria and certain species. The concentration of drugs in a living organism can be answered with calculus.

PPT by – KUSHAL SANGAL XI - A