Definition, Theorem, Worked Examples | Differential Calculus
Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus
Increasing and decreasing functions (or monotonic functions) form an important class of functions in mathematics. These functions occur in various fields
Worked Examples, Exercise with Answers | Differential Calculus
Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus
The derivative f'(c) of a function ƒ at a point c is the slope of the tangent at the point (c, f(c)) on the graph of ƒ given by the equation y = f(x).
Definition, Worked Examples, Exercise with Answers | Differential Calculus
Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus
Certain combinations of exponential functions ex and e-x are called hyperbolic functions. They occur frequently in mathematical and engineering applications.
Definition, Worked Examples, Exercise with Answers | Differential Calculus
Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus
We have seen differentiation of a function given in explicit form y = f(x) and in implicit form F(x, y) = 0.
Worked Examples | Differential Calculus
Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus
When the given function f(x) is a complicated expression, we take natural logarithm to simplify the function and then differentiate it with respect to x.
Worked Examples | Differential Calculus
Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus
So far, we have seen differentiation of function given by equations of the form y = f(x), where y is written explicitly in terms of x.
Trigonometric Functions, Worked Examples, Exercise with Answers | Differential Calculus
Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus
Worked Examples, Exercise with Answers: Derivative of Inverse Functions: Matrices and Calculus: Differential Calculus
Worked Examples, Exercise problems with Answers | Differential Calculus
Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus
Worked Examples, Exercise with Answers: Chain Rule or Derivative of Composite Function: Matrices and Calculus: Differential Calculus
Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus
Worked Examples: Matrices and Calculus: Differential Calculus
Definition, Theorem, Solved Example Problems | Differential Calculus
Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus
Intuitively, a function is derivable or differentiable at a point c if the graph of the function in a neighbourhood of c is a smooth curve without sudden changes in the direction of the graph.
Definition, Theorem, Solved Example Problems | Differential Calculus
Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus
Intuitively, a function is continuous at a point or continuous in an interval if its graph has no break at the point or in the interval.
Definition, Theorem, Solved Example Problems | Differential Calculus
Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus
The essential idea of limit of a function is “nearness" to a point.