Find derivative Calculus, #54?

find the derivative of the function.

h(t)=2cot^2 (pi(t)+2)

plese show out the steps so i can understand, Thanks!

1 Answer

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  • morgan
    Lv 7
    1 decade ago
    Favorite Answer

    Given:

    h(t) = 2 * cot^2 (pi(t)+2)

    Rewriting to make the exponent a little more obvious:

    h(t) = 2 * ( cot(pi(t)+2) )^2

    Taking the derivative, using the chain rule (two levels):

    h'(t) = 4 * ( cot(pi(t)+2) )^1 * (-csc^2(pi(t)+2)) * pi

    Simplify:

    h'(t) = -4pi * ( cot(pi(t)+2) ) * (csc^2(pi(t)+2))

    h'(t) = -4pi * ( cos(pi(t)+2)/sin(pi(t)+2) ) * (1/sin^2(pi(t)+2))

    h'(t) = -4pi * ( cos(pi(t)+2) / sin^3(pi(t)+2) )

    Source(s): Derivative of cot(x) = -csc^2(x) dx http://www.math.com/tables/derivatives/more/trig.h...
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