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Derivatives of Functions in Parametric Form Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Derivatives of Functions in Parametric Form Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is a parametric form of a function?
Ans. Parametric form is a way to represent a function using different variables, typically denoted by a parameter. Instead of expressing the function directly in terms of one variable, it is expressed as a set of equations, each describing how the variables change with respect to the parameter.
2. How do you find the derivative of a function in parametric form?
Ans. To find the derivative of a function in parametric form, you can use the chain rule. First, differentiate each equation with respect to the parameter. Then, divide the derivatives of each variable by each other to obtain the derivative of the function with respect to the parameter.
3. Can you give an example of finding the derivative of a function in parametric form?
Ans. Sure! Let's consider the parametric equations x = 2t^2 and y = 3t. To find the derivative of y with respect to x, we need to differentiate both equations with respect to t. The derivatives are dx/dt = 4t and dy/dt = 3. Dividing dy/dt by dx/dt, we get dy/dx = (3)/(4t). Therefore, the derivative of y with respect to x is (3)/(4t).
4. What are the advantages of using parametric form in calculus?
Ans. Parametric form allows us to describe curves and functions that cannot be easily expressed using a single equation. It is particularly useful in calculus as it enables us to find important properties such as derivatives and integrals more easily. Additionally, parametric equations provide a more intuitive understanding of how variables change in relation to each other.
5. Can you find the derivative of a function in parametric form using other methods besides the chain rule?
Ans. Yes, there are alternative methods to find the derivative of a function in parametric form. One such method is the implicit differentiation technique, where you treat one variable as the independent variable and differentiate both sides of the equation with respect to it. However, the chain rule is the most commonly used method as it is straightforward and applicable in most cases.
204 videos|288 docs|139 tests

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