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Math Help - derivatives and line tangent help please

  1. #1
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    derivatives and line tangent help please

    Hi, I'm stuck on a couple questions and need major help.

    Find f'(x)

    *I'm guessing taking derivative in respect of x if that makes any difference..

    1. y^2+xy=8
    2. sinx+cosy=y^2

    Also,

    3. Find f'(pi/2) of f(x)=sin(2x)

    4. Find d^2y/dx^2 if x^2+y^2=25 at x=4.

    5. Find f'(-1) if f(x)=3x^2-4x+9


    As for the line tangents... here's the problem I'm stuck with.

    6. Find the equation of the line tangent to f(x)=sinx+cosx+1 at x=pi/2.

    I started solving it by taking the derivative of f(x)=sinx+cosx+1. But I have no idea what to do next.


    Extra problems that I will be extremely grateful for more help...

    7. If f(3)=5 and f'(3)=2, what is the best estimate for f(4)
    8. At what point on the graph y=3x^2-8x+9 is the tangent line parallel to y=4x+3.


    Thank you!!
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  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
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    Pblms 1,2, and 4 involve implicit differentiation-- the basic rules are:

    1. When diff a fn of x do it normally
    2. When diff a fn of y diff wrt to y and multiply by y '

    I'll do 1) and leave the other 2 for you

    y^2 + xy = 8

    2y y ' + y + xy' = 0

    y ' (2y +x) = -y

    y ' = -y /(2y+x)

    3,5, and 8 are fairly simple derivatives you should be able to do them

    6 and 7 involve the equation of a tangent line

    the formula for a tangent line at (a,f(a)) is

    y= f ' (a) (x-a) + f(a)
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