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(a) If $ f(x) = e^x $ cos $ x, $ find $ f'(x) $ and $ f"(x). $(b) Check to see that your answers to part (a) are reasonable by graphing $ f, f,' $ and $ f". $

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00:58

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

Campbell University

Oregon State University

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.

01:03

(a) If $f(x)=e^{x} \cos x,…

02:18

02:21

(a) If $ f(x) = (x^2 - 1) …

02:22

$$\begin{array}{l}{\text {…

03:59

(a) If $f(x)=\sec x-x,$ fi…

02:04

(a) If $ f(x) = $ sec $ x,…

02:09

(a) If $ f(x) = e^x/ (2x^2…

04:20

02:38

$\begin{array}{l}{\text { …

03:49

(a) If $ f(x) = (x^3 - x)e…

03:45

07:55

(a) If f(x) = x2 ? 1/x…

it's queer. So then you read here. So we have. Why is equal to eat the X go sign. So using the product rule for the first derivative, we get the derivative or eat the X, which is each the ex turns co sign and then we take the derivative of co sign, which is negative sign times each of X. This gives us each the eggs terms CO signed minus sign. We're going to start with the second derivative, So we're gonna use the product rule again when we go eat to the eggs. Times Co sign minus sign Derivative plus the derivative of E to the X Times CO sign minus sign. This gives us eat the axe times negative sign minus co sign plus E to the X terms CO sign minus sign, which gives us negative to e to the X sign report be we're gonna do a graft. So we're gonna start with our original equation who looks something like this, Then our first year of it is then our second derivative. You let me fix this. Look, I'm doing We're like that

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