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Punkyc7
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find the directional derivative of z=2x^2-y^3 at (1,1)
is it just <4,-3>
is it just <4,-3>
Punkyc7 said:so then how would you go about finding it because where not comparing it with another point... is it just 1
Punkyc7 said:u-1, v-1 and you would dot that with our gradient
Punkyc7 said:we would have to make those unit vector though
A directional derivative is a mathematical tool used in multivariable calculus to determine the rate of change of a function in a specific direction. It measures how a function changes over a specific direction or vector.
The directional derivative is calculated by taking the dot product of the gradient of the function and a unit vector in the desired direction. This results in a single scalar value representing the rate of change of the function in that direction.
Directional derivatives are useful in various fields such as physics, engineering, and economics. They can help in determining the direction in which a system is moving or changing, and can aid in optimizing processes or predicting future outcomes.
Yes, a directional derivative can be negative. A negative directional derivative indicates that the function is decreasing in the given direction, while a positive directional derivative indicates an increase in the function in that direction.
The direction of the vector affects the directional derivative as it determines the direction in which the function is being evaluated. Changing the direction of the vector will result in a different directional derivative, as it represents the rate of change in a specific direction.