Continuity of a function is the characteristic of a function by virtue of which, the graphical form of that function is a continuous wave.
A function is differentiable at a point when there's a defined derivative at that point. It means the slope of the tangent line of points from left is approaching the same value as the slope of the tangent of points from the right.
A differentiable function is a function whose derivative exists at each point in its domain. Students go on to learn about continuity, algebra of continuous function, definition and meaning of differentiability, derivatives of composite functions, derivative of implicit functions. The derivative of inverse trigonometric functions, exponential and logarithmic functions, logarithmic differentiation, derivatives of functions in parametric forms, second-order derivatives, mean value theorem via miscellaneous examples. Here, students can find the exercises explaining these concepts properly with solutions. Topics Covered:
Continuity and differentiability, the derivative of composite functions, chain rule, the derivative of inverse trigonometric functions and derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second-order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.