The derivative is defined as something which is based on some other thing. In Mathematics, Derivative is an expression that gives the rate of change of a function with respect to an independent variable. Derivatives have various applications in Mathematics, Science, and Engineering. We’ll learn about these application of derivatives in the topics below.
- Rate of Change of Quantities
- Approximations
- Increasing and Decreasing Functions
- Maxima and Minima
- Tangents and Normals
FAQs on Application of Derivatives:
Question 1: What are the uses of the derivatives?
Answer: The derivatives are useful as they symbolize slope, we can use them for finding the maxima and minima of various functions. We can also use them to describe how much a function is getting changed.
Question 2: What is the differential calculus and its applications?
Answer: Mathematically, differential calculus is said to be a subfield of the calculus concerned with the study of the proportions at which the quantities are changed. The main objects of study in the differential calculus are the derivatives of a function.
Question 3: What is the application of the limits?
Answer: In the mathematics subjecta limit is the value that a function approaches as the input.
Question 4: What is the product rule for the derivatives?
Answer: The product rule says that ‘if the t2 parts of the sequence are being multiplied with each other. Moreover, the chain rule says that ‘if these are being composed’. For example, to find out the derivative of ‘f(x) = x² sin(x)’, we apply the product rule and for finding out the derivative of ‘g(x) = sin(x²)’ we apply the chain rule.