Derivatives of Radical Functions | Summary and Q&A

TL;DR

Learn how to find the derivative of radical functions by rewriting them as rational exponents, applying the power rule, and utilizing the chain rule.

Key Insights

• ❓ Radical functions can be rewritten as rational exponents to find their derivatives.
• 😑 The power rule is applied when differentiating expressions with rational exponents.
• 📏 The chain rule is used for differentiating composite radical functions.
• 😫 Set your answer in radical form unless specifically instructed to rationalize the denominator.
• 😑 Simplify the expression after finding the derivative to get the final result.
• ❓ Practice with different examples to improve understanding of finding the derivative of radical functions.
• 📏 The power rule and chain rule are fundamental concepts in calculus.

Transcript

today we're going to talk about how to find the derivative of radical functions so let's start with something simple what is the derivative of the square root of x go ahead and try that what do you think we need to do here the first thing we need to do is we need to rewrite the expression the square root of x is basically x to the one half the inde... Read More

Questions & Answers

Q: How do you rewrite a radical function as a rational exponent?

To rewrite a radical function, such as the square root of x, as a rational exponent, use the index number as the denominator and the exponent as the numerator. For example, the square root of x can be written as x^(1/2).

Q: What is the power rule for finding the derivative?

The power rule states that the derivative of x to the n is n times x to the n-1. For example, the derivative of x^3 is 3x^2.

Q: How is the chain rule used in finding the derivative of radical functions?

The chain rule is used when differentiating composite functions. To use the chain rule, differentiate the outside function and keep the inside function the same, then multiply by the derivative of the inside function.

Q: How do you simplify the derivative of a radical function?

After finding the derivative using the power rule and the chain rule, simplify the expression by combining like terms and converting any rational exponents back to radical form.

Summary & Key Takeaways

• Radical functions can be rewritten as rational exponents.

• The power rule states that the derivative of x to the n is n times x to the n-1.

• The chain rule is used to differentiate composite functions, where the derivative of the outside function is multiplied by the derivative of the inside function.