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Find the first and second derivatives of the function. Check to see that your answers are reasonable by comparing the graphs of $ f, f', $ and $ f". $$ f(x) = 2x - 5x^{3/4} $

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00:37

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Campbell University

Baylor University

Idaho State University

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.

02:15

Find the first and second …

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01:25

Find the first, second, an…

Hey, it's clear. So when you read here so we have a of X is equal to two X minus five X to the 34 it's then we have our derivative just equal to two minus 15 over four x to the negative 1/4. And to find the second derivative, we just have to differentiate our first to get 15 over 16 x to the negative five boards. We're going to graph our original derivative and second derivative. It's our original Looks like this and our second derivative well look like this. And then our last graph for our stuck in derivative looks like this.

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