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Find the first and second derivatives of the function.$ G(r) = \sqrt{r} + \sqrt[3]{r} $

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00:46

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Missouri State University

University of Nottingham

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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he It's clear. So when you read here so we have our original function. G a r. She's equal to our The one have plus our two the 1/3. And then we're going to apply to some and par ral to differentiate. We get 1/2 our it's a negative one house close 1/3 are than negative 2/3. And for the second derivative, we're gonna different sheet. The first derivative, we're gonna apply to some and constant part multiple rule and differentiate the rest using the power off. So I get half negative, half hard to the negative three house plus 1/3 negative 2/3 are too negative. 5/3. This is equal to negative 1/4 hard to the negative three house plus negative to ninth are to the negative 5/3

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