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with derivatives?

Derivatives are fundamental to the solution of problems in calculus and differential equations.

Derivatives course

In mathematics, the derivative is a fundamental tool that quantifies the sensitivity of change of a function's output with respect to its input.
The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.

Video 1

Video introduction

Video 2

Derivative of a constant

Video 3

Derivative of a power

Video 4

Derivative of a constant by function

Video gallery

01. Video introduction

01. video introduction

02. Derivative of a constant

03. Derivative of a power

04. Derivative of a constant by function

Concepts


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Derivative

A derivative is a fundamental concept in calculus that describes how a function changes in relation to its independent variables. In simplest terms, the derivative measures the rate of change or slope of a function at a specific point.

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Applications

  • Maximums and minimums: Find maximum or minimum values ​​of a function.
  • Optimization: Solve problems to maximize or minimize resources.
  • Velocity and acceleration: In physics, the derivative of velocity is acceleration.
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    Critical Points

  • A function is differentiable at a point if its derivative exists at that point.
  • Note: If a function has a "peak" or a jump, it is not differentiable at that location.


  • Derivative of a constant





    Derivative of a sum





    Derivative of X to the nth power



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