definition of the derivative with square root (and conjugate) | Summary and Q&A

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January 10, 2015
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blackpenredpen
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definition of the derivative with square root (and conjugate)

TL;DR

The video explains how to find the derivative of sqrt(1-2x) using the first principle, step by step.

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Key Insights

  • ❓ The first principle definition is a fundamental concept in calculus for finding the derivative of a function.
  • 🥡 The process of finding the derivative involves substitution, simplification, and taking the limit.
  • ✖️ Multiplying the numerator and denominator by the conjugate helps simplify the equation.
  • 🍉 Canceling out terms that cancel each other out is an important step in simplifying the equation.

Transcript

we will use the definition of derivative (first principle) to find the derivative of sqrt(1-2x) physical education let's take a look of how  this enthalpy of H looks like so that's the   function let me to yamazaki f of X we know  that's equal to square root of 1 minus 2x   and then F of a plus h you want you to do  that all we need to do is plug i... Read More

Questions & Answers

Q: What is the first principle definition of a derivative?

The first principle definition states that the derivative of a function f of x is calculated by taking the limit as h approaches 0 of [f(x + h) - f(x)] / h.

Q: How do we find the derivative of sqrt(1-2x) using the first principle?

To find the derivative of sqrt(1-2x), we start by substituting f(x + h) and f(x) into the first principle equation. Then, we simplify the equation by multiplying the numerator and denominator by the conjugate. Finally, we take the limit as h approaches 0 and plug in the remaining values to find the derivative.

Q: What are the steps involved in simplifying the equation?

The steps involved in simplifying the equation include multiplying the numerator and denominator by the conjugate, canceling out the terms that cancel each other, and plugging in 0 for the remaining variables. This simplification process helps us find the final answer.

Q: What is the final answer for the derivative of sqrt(1-2x)?

The final answer for the derivative of sqrt(1-2x) using the first principle is -1 / sqrt(1-2x).

Summary & Key Takeaways

  • The video demonstrates the process of finding the derivative of sqrt(1-2x) using the first principle definition.

  • It explains each step, showing how to substitute values and simplify the equation.

  • The final answer is derived by plugging in the values and simplifying the expression.

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