Differential Calculus
- Differential calculus is used to solve the problem of calculating the rate at which a function changes in relation to other variables.
- To obtain the optimal answer, derivatives are utilized to determine a function’s maxima and minima values.
- It primarily handles variables like x and y, functions like f(x), and the variations in x and y that follow.
- dy and dx are used to symbolize differentials.
- The process of differentiating allows us to compute derivatives. The derivative of a function is given by dy/dx or f’ (x).
Let’s go over some of the important subjects covered in basic differential calculus.
Limits
Limit is used to calculate the extent of closeness to any term or upcoming term. A limit is denoted with the help of the limit formula as,
limx⇢c f(x) = A
This expression is understood as “the limit of f of x approaches c equals A”.
More articles on Limits, to get better understanding:
Derivatives
The instantaneous rate at which one quantity changes in relation to another is represented by derivatives. The representation of a function’s derivative is:
limx⇢h [f(x + h) – f(x)]/h = A
More articles on Derivatives, to get better understanding.
- Introduction to Derivatives
- Average and Instantaneous Rate of Change
- Algebra of Derivative of Functions
- Product Rule – Derivatives
- Quotient Rule
- Derivatives of Polynomial Functions
- Derivatives of Trigonometric Functions
- Power Rule in Derivatives
- Application of Derivatives
- Applications of Power Rule
- Continuity and Discontinuity
- Differentiability of a Function
- Derivatives of Inverse Functions
- Derivatives of Implicit Functions
- Derivatives of Composite Functions
- Derivatives of Inverse Trigonometric Functions
- Exponential and Logarithmic Functions
- Logarithmic Differentiation
- Proofs for the derivatives of eˣ and ln(x) – Advanced differentiation
- Derivative of functions in parametric forms
- Second-Order Derivatives in Continuity and Differentiability
- Rolle’s and Lagrange’s Mean Value Theorem
- Mean value theorem – Advanced Differentiation
Continuity
A function f(x) is said to be continuous at a particular point x = a if the following three conditions are satisfied –
- f(a) is defined
- limx⇢af(x) exists
- limx⇢a– f(x) = limx⇢a+ f(x) =f(a)
Continuity and Differentiability
A function is always continuous if it is differentiable at any point, whereas the vice-versa condition is not always true.
More articles on Continuity and Differentiability, to get better understanding
Calculus | Differential and Integral Calculus
In mathematics, Calculus deals with continuous change. It is also called infinitesimal calculus or “the calculus of infinitesimals”. The Two major concepts of calculus are Derivatives and Integrals.
- The derivative gives us the rate of change of a function. It describes the function at a particular point while the integral gives us the area under the curve.
- The integral gives us the area under the curve. Integral gathers the different values of a function over a number of values.
In general, classical calculus Calculus is the study of the continuous change of functions. In this article, we have provided everything related to Math Calculus for Beginners. Definition, examples, and practice questions will help you not only learn calculus theory but also practice calculus.
Table of Content
- What is Calculus?
- Basic Calculus
- Calculus Topics
- Calculus Functions
- Types of Calculus
- Differential Calculus
- Integral Calculus
- Calculus Formulas
- Advanced Calculus
- Applications of Calculus
- Sample Calculus Problems with Solutions
- Practice Questions on Calculus
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