![]() It begins with an in-depth explanation of differential calculus, including limits, the product and quotient rules, the chain rule, derivatives of different functions, and optimization. ![]() This guide mainly focuses on the topics learned in calculus I. ![]() For Newton, calculus was necessary for describing the physics of gravity that he was simultaneously studying. Calculus AB will cover the equivalent of calculus I while calculus BC will cover most of calculus I and II.Īlthough Isaac Newton generally gets the credit “ inventing” or “ discovering” calculus, the concepts of calculus were derived independently by Isaac Newton and Gottfried Wilhelm Leibnitz at about the same time. Alternatively, a human resource director can use it to figure out the minimum number of employees needed for a new site to operate.Ĭalculus is often divided up as calculus I, II, and III.Ĭalculus I will typically cover both differential and integral calculus like this guide.Ĭalculus II explores more complex topics of integral calculus and series and sequences, while calculus III is normally the study of multi-variable calculus.Īlternatively, many high schools in the United States break calculus up as calculus AB and calculus BC. The word itself comes from a Latin word meaning “ pebble” because pebbles used to be used in calculations.Ĭalculus has applications in both engineering and business because of its usefulness in optimization.įor example, an engineer could use calculus to find out the least amount of material needed for a machine to still operate correctly. It uses concepts from algebra, geometry, trigonometry, and precalculus. The differentiation of a constant is 0 as per the power rule of differentiation.Calculus is the study of things in motion or things that are changing. What is The Differentiation of a Constant? To know more applications of differentiation, click here. We use the differentiation formulas to find the maximum or minimum values of a function, the velocity and acceleration of moving objects, and the tangent of a curve. What Are The Applications of Differentiation Formulas? Constant Rule: y = k f(x), k ≠ 0, then d/dx(k(f(x)) = k d/dx f(x).Chain Rule: Let y = f(u) be a function of u and if u=g(x) so that y = f(g(x), then d/dx(f(g(x))= f'(g(x))g'(x).Quotient Rule: If y = u(x) ÷ v(x), then dy/dx = (v.du/dx- u.dv/dx)/ v 2.Product Rule: If y = u(x) × v(x), then dy/dx = u.dv/dx + v.du/dx.Sum Rule: If y = u(x) ± v(x), then dy/dx = du/dx ± dv/dx. ![]() The differentiation rules are power rule, chain rule, quotient rule, and the constant rule. There are different rules followed in differentiating a function. We know, slope of the secant line is \(\dfraccos(x+Δx) = cos x\)] What Are The Differentiation Rules in Calculus? The slope of a curve at a point is the slope of the tangent line at that point. Take another point Q with coordinates (x+h, f(x+h)) on the curve. Let us take a point P with coordinates(x, f(x)) on a curve. The first principle of differentiation is to compute the derivative of the function using the limits. ![]() The geometrical meaning of the derivative of y = f(x) is the slope of the tangent to the curve y = f(x) at ( x, f(x)). ![]()
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