A community for students.
Here's the question you clicked on:
 0 viewing
 2 years ago
On section 4 of part A of the first unit (wow that is a mouthful) how are we expected to know how to calculate the derivative of sin 2x? On the worked example, we need to know this somehow.
 2 years ago
On section 4 of part A of the first unit (wow that is a mouthful) how are we expected to know how to calculate the derivative of sin 2x? On the worked example, we need to know this somehow.

This Question is Open

MattBenjamins
 2 years ago
Best ResponseYou've already chosen the best response.3You are not. To calculate the derivative of sin2x you need to know the derivative of sinx and you need to know about the chain rule. Both are explained later in the course (sessions 7 and 11 respectively). It's a little strange that this problem is included before those sessions but if you look at them you should be able to understand it.

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.0Method 1: By Chain Rule If y = sin 2x then let u = 2x and then y = sin u. Now du/dx = 2 and dy/du = cos u [∵ the graph of the derivative (slope) of the sine function is the cosine function]. By chain rule in Leibniz notation, dy/dx = (dy/du)(du/dx) Thus dy/dx = 2(cos u) Replacing u with 2x, we obtain dy/dx = 2(cos 2x) Method 2: Taking the derivative of the six trigonometric functions. Know that d(sin x)/dx = cos x d(cos x)/dx = sin x d(tan x)/dx = sec²x d(csc x)/dx = (csc x)(cot x) d(sec x)/dx = (sec x)(tan x) Rule: To differentiate on of the six trigonometric functions: i). multiply the derivative of the angle by the amplitude, ii). multiply this product by the derivative of the respective trig function. Remember to never change the angle. Thus if y = sin 2x then dy/dx = [d(2x)/dx](1)(cos, the derivative of sin, and never change the angle) ∴ dy/dx = 2(cos 2x) Note you may also find the derivative from the definition of the derivative.

toddcarnes
 2 years ago
Best ResponseYou've already chosen the best response.0Watch the recitation video for the class titled "Derivatives of Sine and Cosine". Its available for download at http://archive.org/details/MIT18_01SCF10/ or you can watch it online at http://www.youtube.com/watch?v=BbbgJdOqig&feature=plcp

mzirino
 2 years ago
Best ResponseYou've already chosen the best response.0I believe your double angle formulas from trigonometry will tell you that sin 2x = 2sinx cosx which you can differentiate via the product rule.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.