Which derivative rule would I use?

if I know the derivative of sine and cosine I could find the derivative directly of the tangent with what rule?

Chain? power? Product? or quotient? 

2 Answers

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  • Philip
    Lv 6
    5 months ago
    Favorite Answer

    1) Quotient rule: {d/dx}(u/v) = (1/v^2)[v(du/dx) - u(dv/dx)]. For tan = sin/cos we 

    have u = sin and v = cos, (du/dx) = cos, (dv/dx) = -sin. Then {d/dx}(tan) =;

    (1/cos^2)[cos(cos) -sin(-sin)] = 1/cos^2 = sec^2.

    2) Product rule combined with chain & power: We write tan = sin*cos^-1. Then u = sin & v = cos^-1. {d/dx}(u*v) = [u(dv/dx) + v(du/dx)]. (dv/dx) = -cos^-2(-sin).

    (du/dx) = cos. Then {d/dx}(tan) = [sin(sincos^-2) + (cos^-1)cos] = 1+sin^2/cos^2

    = (sin^2+cos^2)/cos^2 = 1/cos^2 = sec^2.

  • 5 months ago

    Use the quotient rule since tan(x) = sin(x) / cos(x).

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