Understanding directional derivatives is crucial in multivariable calculus, especially when determining the maximum value in a particular direction. Our Maximum Value of Directional Derivative Calculator simplifies this process, allowing users to quickly find the maximum value with ease.
Formula: The directional derivative at a point (x₀, y₀) in the direction of a unit vector v = ⟨a, b⟩ is given by the formula:
��(�0,�0;�)=��(�0,�0)⋅�+��(�0,�0)⋅�Df(x0,y0;v)=fx(x0,y0)⋅a+fy(x0,y0)⋅b
where ��fx and ��fy are the partial derivatives of the function f(x, y) with respect to x and y, respectively.
How to Use:
- Enter the function f(x, y) in the designated field.
- Input the point (x₀, y₀) in the provided space.
- Click the “Calculate” button to obtain the maximum value of the directional derivative.
- View the result in the output field.
Example: For example, to find the maximum directional derivative of the function �(�,�)=�2+�2f(x,y)=x2+y2 at the point (1, 2) in the direction of the vector ⟨3, 4⟩, enter the function as “x^2 + y^2” and the point as “(1, 2)”.
FAQs:
- Q: What is a directional derivative? A: A directional derivative measures the rate at which a function changes at a given point in a specified direction.
- Q: How do I calculate the partial derivatives? A: Differentiate the function with respect to each variable separately.
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Conclusion: Our Maximum Value of Directional Derivative Calculator simplifies the process of finding the maximum value in a specific direction. Whether you’re a student or a professional, this tool provides quick and accurate results, saving time and effort in multivariable calculus calculations.