1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Derivative Question

  1. Dec 15, 2009 #1
    I am studying this from a book I found online, and I need a little bit of help.

    1. The problem statement, all variables and given/known data
    Find the derivative when [itex]y(x)=\sin x[/itex]

    3. The attempt at a solution

    [itex]\frac{dy}{dx} \ = \ limit \ of \ \frac {\Delta y}{\Delta x} \ = \ \lim h \rightarrow 0 \ \frac{\sin(x+h)-\sin x}{h}[/itex]

    [itex]\sin(x+h)=\sin x \cos h + \cos x \sin h[/itex]

    [itex]\frac{\Delta y}{\Delta x} \ = \ \frac {\sin x \cos h + \cos x \sin h-\sin x}{h} \ = \ \sin x ( \frac{\cos h-1}{h}) + \cos x (\frac{\sin h}{h})[/itex]
     
  2. jcsd
  3. Dec 15, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    now take the limit as h→0, what does sinh/h tend to? and what does (cosh-1)/h tend to?
     
  4. Dec 16, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Strictly speaking, how you do that depends upon what your definitions of "sine" and "cosine" are- and there are several possible. What definitions are you using?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Derivative Question
  1. Derivative homework (Replies: 3)

  2. Derivation help! (Replies: 8)

  3. Algebraic Derivative (Replies: 10)

  4. Logarithmic derivative (Replies: 7)

Loading...