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Math Help - Trignometric functions derivative

  1. #1
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    Trignometric functions derivative

    Find the derivative of the function

    1.) f(x)=sqrt(cosx+sinx)

    f(x)= (cosx+sinx)^1/2
    f'(x)= 1/2(cosx+sinx)^-1/2 d/dx (cosx+sinx)
    = ???

    2.) f(x)=e^(tanx+secx)
    f'(x)=e^(tanx+secx) 。d/dx(tanx+secx)
    =???

    3.) f(x)= ln(sin^-1 (x))

    Find dy/dx by implicit differentation

    1.) x sec(y)=ln(sinx)

    The text in the red is what i got so far..then i got stuck..can anyone help me?
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  2. #2
    MHF Contributor kalagota's Avatar
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    Taguig City, Philippines
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    Quote Originally Posted by lemontea View Post
    Find the derivative of the function

    1.) f(x)=sqrt(cosx+sinx)

    f(x)= (cosx+sinx)^1/2
    f'(x)= 1/2(cosx+sinx)^-1/2 d/dx (cosx+sinx)
    = ???

    2.) f(x)=e^(tanx+secx)
    f'(x)=e^(tanx+secx) 。d/dx(tanx+secx)
    =???
    yes.. and how do you find the derivative of the sum?
    \frac{d}{dx}\sin x = ?
    \frac{d}{dx}\cos x = ?
    \frac{d}{dx}\tan x = ?
    \frac{d}{dx}\csc x = ?
    \frac{d}{dx}\sec x = ?
    \frac{d}{dx}\cot x = ?

    surely, you have been already taught about these..
    Quote Originally Posted by lemontea View Post
    3.) f(x)= ln(sin^-1 (x))

    Find dy/dx by implicit differentation
    so, let y = \ln (\sin^{-1} x) \Longleftrightarrow e^y = \sin^{-1} x

    Quote Originally Posted by lemontea View Post
    1.) x sec(y)=ln(sinx)

    The text in the red is what i got so far..then i got stuck..can anyone help me?
    do you already know \frac{d}{dx}(\ln x)?
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  3. #3
    Super Member
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    Perhaps you might have forgotten to write it down in the lecture or the book doesn't mention it in any way Just have a look at this:
    World Web Math: Rules of differentiation
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