Derivatives of logarithmic functions pdf
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One to one and onto functions, composite functions, inverse of a function. Definition, range, domain, principal value branch. Elementary properties of inverse trigonometric functions. Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Adjoint and inverse of a square matrix.
Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Derivatives of logarithmic and exponential functions. Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the types given in the syllabus and problems based on them. Basic properties of definite integrals and evaluation of definite integrals. Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given.
Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type given in the syllabus. Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector.
Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Distance of a point from a plane. Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Find out how easy it is to get started.
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Follow the link for more information. This article is about the term as used in calculus. For a less technical overview of the subject, see differential calculus. The graph of a function, drawn in black, and a tangent line to that function, drawn in red. The slope of the tangent line is equal to the derivative of the function at the marked point. Derivatives are a fundamental tool of calculus.
The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. Derivatives may be generalized to functions of several real variables. The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration.
Differentiation is the action of computing a derivative. This gives an exact value for the slope of a line. Two distinct notations are commonly used for the derivative, one deriving from Leibniz and the other from Joseph Louis Lagrange. The above expression is read as “the derivative of y with respect to x”, “d y by d x”, or “d y over d x”.
The oral form “d y d x” is often used conversationally, although it may lead to confusion. Lagrange’s notation is sometimes incorrectly attributed to Newton. The most common approach to turn this intuitive idea into a precise definition is to define the derivative as a limit of difference quotients of real numbers. This is the approach described below. These lines are called secant lines.