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| Introduction |
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| After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable. |
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| The derivative, measures the rate at which the dependent variable changes with respect to the independent variable. It is one of the most important ideas in Calculus. The differentiation of functions are widely used in science, economics, medicine and computer science. |
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| Differentiation is a major tool to find out the velocity and acceleration of fast moving objects. A vigorous study of differentiation helps in curve-tracing. It was Kepler who concluded that planets revolve round the Sun in elliptic orbits. But he could not give a logical reasoning for this because the methods of Calculus was not known by then. Economists use differentiation to maximise profit with minimum cost. Differentiation is also used to study the behavior of machinery. What could be the shape of a least expensive machine, which can work effectively? Calculus enables to estimate the reduction in water levels as water is pumped out of tank; to predict the consequences of making errors in measurements. |
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| Sir Isaac Newton and Leibnitz share the credit of initiating development in the subject matter of derivability. |
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| In this chapter, we learn the concept of derivability, process of differentiation, methods of differentiation and also obtain the second order derivatives of functions. |
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