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(a) Graph the function $ g(x) = e^x - 3x^2 $ in the viewing rectangle [-1,4] by [-8,8].(b) Using the graph in part (a) to estimate slopes, make a rough sketch, by hand, of the graph of $ g' $. (c) Calculate $ g'(x) $ and use this expression, with a graphing device, to graph $ g' $. Compare with your sketch in part (b).

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00:18

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Missouri State University

Campbell University

Harvey Mudd College

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.

04:41

(a) Graph the function $g(…

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(a) Use a graphing calcula…

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(a) Graph the function…

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Graph $f$ in the viewing r…

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(a) Graph $f$ using a grap…

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it's clear. So when you read here so we have f of facts is equal to eat The axe minus three X squared star graph will look something like this 1234 and then part B We're going to draw another graft this time are derivative And I look like this goes down the X axis and backup and then part see So we're given our original equation and we're gonna differentiate I get Do you ever d x for eat? The X minus three X square is equal to eat the excellent of six acts in the graph Fun. I was down and back up.

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