Register to reply

Find the derivative and the domain of the derivative (trig funtions)

by Absolutism
Tags: derivative, domain, funtions, trig
Share this thread:
Absolutism
#1
Nov10-11, 01:04 PM
P: 28
1. The problem statement, all variables and given/known data

f(x)=sin(2x+5)

2. Relevant equations

I am supposed to find the derivative, and the domain of it. The problem is that I cannot deal with the simplification of it.

3. The attempt at a solution

As far as I know, I am suppsosed to use f(x+h)-f(x)/h
= sin(2(x+h)+5)-(sin(2x+5))/h

I tried expanding what's inside, as in sin(2x+2h+5)-sin(2x+5)/h
But that doesn't seem to lead to a solution
Phys.Org News Partner Science news on Phys.org
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces
Mark44
#2
Nov10-11, 01:23 PM
Mentor
P: 21,216
Quote Quote by Absolutism View Post
1. The problem statement, all variables and given/known data

f(x)=sin(2x+5)

2. Relevant equations

I am supposed to find the derivative, and the domain of it. The problem is that I cannot deal with the simplification of it.

3. The attempt at a solution

As far as I know, I am suppsosed to use f(x+h)-f(x)/h
= sin(2(x+h)+5)-(sin(2x+5))/h

I tried expanding what's inside, as in sin(2x+2h+5)-sin(2x+5)/h
But that doesn't seem to lead to a solution
Are you certain that you have to use the limit definition of the derivative here? Have you learned the chain rule yet?
Absolutism
#3
Nov10-11, 01:28 PM
P: 28
I have learned the chain rule, and I am certain I am supposed to use the limit definition in this question

Mark44
#4
Nov10-11, 02:08 PM
Mentor
P: 21,216
Find the derivative and the domain of the derivative (trig funtions)

OK, then I think you'll need to use the sum identity for sine: sin(A + B) = sin(A)cos(B) + cos(A)sin(B).

You will probably need to use a couple of limit formulas as well:
[tex]\lim_{h \to 0}\frac{sin(h)}{h} = 1[/tex]
[tex]\lim_{h \to 0}\frac{cos(h) - 1}{h} = 0[/tex]
lurflurf
#5
Nov10-11, 03:50 PM
HW Helper
P: 2,263
recall the trigonometric identity
sin(2(x+h)+5)-(sin(2x+5))=2 sin(h) cos(h+2 x+5)
or in general
sin(A)-sin(B)=2 sin(A/2-B/2) cos(A/2+B/2)
and use the facts that
cosine is continuous
sin'(0)=1
Absolutism
#6
Nov11-11, 02:38 PM
P: 28
Quote Quote by Absolutism View Post
I have learned the chain rule, and I am certain I am supposed to use the limit definition in this question
Quote Quote by Mark44 View Post
OK, then I think you'll need to use the sum identity for sine: sin(A + B) = sin(A)cos(B) + cos(A)sin(B).

You will probably need to use a couple of limit formulas as well:
[tex]\lim_{h \to 0}\frac{sin(h)}{h} = 1[/tex]
[tex]\lim_{h \to 0}\frac{cos(h) - 1}{h} = 0[/tex]
Quote Quote by lurflurf View Post
recall the trigonometric identity
sin(2(x+h)+5)-(sin(2x+5))=2 sin(h) cos(h+2 x+5)
or in general
sin(A)-sin(B)=2 sin(A/2-B/2) cos(A/2+B/2)
and use the facts that
cosine is continuous
sin'(0)=1

Am I supposed to solve for when a --> 0?

That's what I did.

sin(2x+5)-sin(2a+5) = 2sin ((x-a)/2) cos ((x+a)/2)

= sin (2x+5)-sin (5) = 2sin (x/2) cos (x/2)

Then the x was = 0

I am not sure I am on the right track. The derivative is cos(2x+5)(2) .-. I am not supposed to achieve a value. So was I supposed to keep the a?
SammyS
#7
Nov11-11, 04:32 PM
Emeritus
Sci Advisor
HW Helper
PF Gold
P: 7,795
Quote Quote by Absolutism View Post
Am I supposed to solve for when a --> 0?

That's what I did.

sin(2x+5)-sin(2a+5) = 2sin ((x-a)/2) cos ((x+a)/2)

...
Actually sin(2x+5)-sin(2a+5) = 0

You need to look at sin((2x+5)+h)-sin(2a+5) = 2sin (h/2) cos ((2x+5)+h/2) .
Absolutism
#8
Nov11-11, 04:38 PM
P: 28
Quote Quote by SammyS View Post
Actually sin(2x+5)-sin(2a+5) = 0

You need to look at sin((2x+5)+h)-sin(2a+5) = 2sin (h/2) cos ((2x+5)+h/2) .

Oh. Alright. Thank you very much :]


Register to reply

Related Discussions
Covariant derivate same as normal derivative? Differential Geometry 3
Find the second derivate .(tricky question). Calculus & Beyond Homework 6
Max/min with trig funtions problem Calculus & Beyond Homework 1
Trig Funtions Problems Introductory Physics Homework 4
Questions concerning, logs, rational funtions, and trig. Introductory Physics Homework 3