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Transcript: Math Trivia: Math Trivia: 18 is the only number that is twice the sum of its digits. Any number to the power zero is 1, and zero to any power is 0. The only unanswered question here is what is zero to the power zero? Derivatives - In mathematics, the derivatives of a function a of a real variable measurement the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives Differentiation Rules It has 8 Rules, The constant rule, Sum rule, Difference rule, Product rule, Quotient rule, Constant Multiple rule, Power rule, and Chain rule. Differentiation Rules Rules Constant Rule The rule basically says that when a function is a number times another function, we can essentially ignore that number for derivative purposes Constant Rule Formula of Constant rule: Sum Rule - The derivatives of a sum of functions is the sum of their derivatives Sum Rule Formula of sum rule: Difference Rule - The Difference rule says the derivative of a difference of functions is the difference of their derivatives Difference Rule Formula of difference rule: Product Rule - The Product Rule says that how to differentiate expressions that the two product. Product Rule Formula of Product rule: Quotient Rule Quotient Rule - The quotient rule is a formal rule for differentiating problems where one function is divided by another. Formula of Quotient rule: Constant Multiple Rule - The Constant multiple rule says the derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function. Constant Multiple Rule Formula of Constant Multiple rule: Power Rule - The power rule is a quick tool for finding the derivative of a function. It works whenever you can write the expression so that each term is simply a variable raised to a power. Power Rule Formula of Power rule: Chain Rule - The chain rule is a formula to compute the derivative of a composite function. Chain Rule Formula of Chain rule: Example Differentiation Problem Trigonometric Function In mathematics, the trigonometric functions (also called circular functions, angle functions or trigonometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. Trigonometric Function Formula of Trigonometric functions: Example: Trigonometric problem Real Life Application - Derivatives can use in real life. In measuring business profit if losing , physics, temperature variation , speed such as kph, mph and etc. , distance(km, m). You can use it too in engineering and science. Real Life Application Real Life Application Example 1 Real Life Application example Biology -Derivatives are used in to model population growth, ecosystems, spread of diseases and various phenomena. The area that I will focus particularly is population growth. Suppose n =f(t) is the number of individuals of some species of animal or plant population at time t. Real Life Application Example 2 Real Life Application example Economics -In recent years, economic decision making has become more and more mathematically oriented. Faced with huge masses of statistical data, depending on hundreds or even thousands of different variables, business analysts and economists have increasingly turned to mathematical methods to help them describe what is happening, predict the effects of various policy alternatives, and choose reasonable courses of action from the myriad of possibilities. Among the mathematical methods employed is calculus. In this section we illustrate just a few of the many applications of calculus to business and economics. Limits - In mathematics, a limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. Limits Evaluate Limits - Evaluating Limits. "Evaluating" means to find the value of (think e-"value"-ating) In the example above we said the limit was 2 because it looked like it was going to be. Evaluate Limits Analytically Analytically Example Graphically Example Problem Rational Functions - A rational function is any function which can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K Rational Functions Rational Problem Rational Problem Limits in Real life Real Life Application In real time situation, limit is so useful this is one of the solution to make your work nice. Example in baking, You need to put exact egg to avoid rising to high. You need to put exact amount of sugar to avoid getting diabetes. Example - In a expressway, it has minimum and maximum speed limit, The motorcycle must maintain speed of 60 kph. And a motorcycle must not exceed in maximum speed limit of 100 kph. In a motorcycle Example In cooking
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