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Derivative of a Function Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
FAQs on Derivative of a Function Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is the derivative of a function? |  |
Ans. The derivative of a function represents the rate at which the function is changing at any given point. It measures the slope of the function's graph at that point.
| 2. How is the derivative of a function calculated? | |
Ans. The derivative of a function can be calculated using differentiation rules such as the power rule, product rule, quotient rule, and chain rule. These rules allow us to find the derivative of a function based on its algebraic form.
| 3. What is the significance of the derivative in calculus? | |
Ans. The derivative has several important applications in calculus. It helps us analyze the behavior of functions, find critical points and extreme values, determine the concavity of a function, and solve optimization problems.
| 4. Can the derivative of a function be negative? | |
Ans. Yes, the derivative of a function can be negative. It indicates that the function is decreasing in value as the input increases. The sign of the derivative provides information about the increasing or decreasing nature of the function.
| 5. Is the derivative of a constant function always zero? | |
Ans. Yes, the derivative of a constant function is always zero. Since a constant function has a constant rate of change, its derivative is zero as there is no change in the function's value.
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