Math | Differential Calculus | Derivability and Derivatives | Lect.-4 | Dr. S.S.Bellale | DSCL

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#Derivability and derivative,
Derived function,
Derivability implying continuity,
Geometrical interpretation of a derivative, d
Derivatives of hyperbolic functions,
Derivatives of inverse hyperbolic functions,
Higher order derivatives,
Calculation of the nth derivative,
Determination of nth derivative of rational functions,
nth derivatives of the products of the powers
of sines and cosines,
Leibnitz theorem
Maclaurin’s theorem,
Taylor’s theorem,
Equations of the tangent and normal,
Angle of intersection of two curves,
Length of the tangent,
Normal,
Sub-tangent,
Sub-normal,
Pedal equations
Rolle’s Theorem,
Lagrange’s mean value theorem,
Meaning of sign of derivative,
Graphs of hyperbolic functions,
Cauchy’s mean value theorem,
Generalized mean value theorems
(Taylor’s theorem, Maclaurin’s theorem).

Introduction,
Functions of two variables,
Neighborhood of a point (a,b),
Limit and Continuity,
Partial derivatives,
Geometrical Interpretation,
Homogeneous functions,
Euler’s Theorem on homogeneous function and corollary,
Theorems on total differentials,
Equality of fxy (a, b) and fyx(a, b),
Equality of fxy and fyx,
Taylors theorem for functions of two variables (Only Statement).