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Math Help - [SOLVED] equation of a tangent line

  1. #1
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    Unhappy [SOLVED] equation of a tangent line

    Having a little bit of problem....
    Let c be a nonzero real number. What is the equation of the tangent line to the graphof the function y=sin(x/x+c) at the point x=0.

    i get the derivate of cos(1/1+c) but i really dont think that it right!!! am i am differentiating properly!!!???
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  2. #2
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    \frac{d}{{dx}}\left( {\sin \left( {\frac{x}{{x + c}}} \right)} \right) = \cos \left( {\frac{x}{{x + c}}} \right)\left( {\frac{c}{{\left( {x + c} \right)^2 }}} \right)
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  3. #3
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    simply07!

    Let c be a nonzero real number.
    What is the equation of the tangent line to the graph of the function
    y \:=\:\sin\left(\frac{x}{x+c}\right) at the point x=0.

    i get the derivate of \cos\left(\frac{1}{1+c}\right) but i really dont think that it right!
    am i differentiating properly? . . . . no

    You'd better review the Chain Rule ... and the Quotient Rule.

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    ok i see the mistake... so now to find the value at x = 0, i would simply replace x for 0....

    then my answer woul be 1/c ???
    this make sence but is it right?

    thanks
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  5. #5
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    Quote Originally Posted by simply07 View Post
    ok i see the mistake... so now to find the value at x = 0, i would simply replace x for 0....

    then my answer woul be 1/c ???
    this make sence but is it right?

    thanks
    That's the correct slope of the tangent line. So your tangent line has the slope-intercept form of:
    y = \frac{1}{c} \cdot x + b

    It must pass through the point (0, y(0)), so plug this point in to find b.

    -Dan
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