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What does it mean to derive something mathematically? Review your graphing and exponent skills as you prepare to use them to find a function's slope at any point.
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Illustrated definition of Derivative: The rate at which an output changes with respect to an input. Working out a derivative is called Differentiation...
- Let Us Find A Derivative!
- Derivatives of Other Functions
- Notation
To find the derivative of a function y = f(x)we use the slope formula: Slope = Change in Y Change in X = ΔyΔx And (from the diagram) we see that: Now follow these steps: 1. Fill in this slope formula: ΔyΔx = f(x+Δx) − f(x)Δx 2. Simplify it as best we can 3. Then make Δxshrink towards zero. Like this:
We can use the same method to work out derivatives of other functions (like sine, cosine, logarithms, etc). But using the rules can be tricky! So that is your next step: learn how to use the rules.
"Shrink towards zero" is actually written as a limitlike this: "The derivative of f equals the limit as Δx goes to zero of f(x+Δx) - f(x) over Δx" Or sometimes the derivative is written like this(explained on Derivatives as dy/dx): The process of finding a derivative is called "differentiation".
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Oct 16, 2023 · In mathematics (particularly in differential calculus), the derivative is a way to show instantaneous rate of change: that is, the amount by which a function is changing at one given point. For functions that act on the real numbers, it is the slope of the tangent line at a point on a graph.
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Learn about derivatives as the instantaneous rate of change and the slope of the tangent line. This video introduces key concepts, including the difference between average and instantaneous rates of change, and how derivatives are central to differential calculus.
