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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) = e^x - x^3 $

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00:22

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

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.

02:20

Find the first and second …

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Use the definition of a de…

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Find a function $f$ that h…

01:08

Hey, it's clear. So when you read here is so we have f of X is equal to I need to the ex minus X cubed We could differentiate when we get beat to the ex minus three X square And to get our second derivative, we just differentiate first we gotta eat the X minus six x We're gonna draw our graph up with them all together at once. So original function enough of X while doing black and I'll look like this are derivative is in red and our second derivative is in green.

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