Calculus

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find the derivative of f(x)=tanx-4/secx

I used the quotient rule and got (sec^2x-4)(secx)-(tanx-4)(cosx)/sec^2x but I'm pretty sure that's wrong. Help. Thanks.

  • Calculus -

    It is not clear what your expression really is, there are two possibilities. In both cases, it pays to do a little simplification before differentiating.

    If f(x)=(tan(x)-4)/sec(x)
    then
    f(x)
    =tan(x)*cos(x) - 4 cos(x)
    =sin(x) - 4 cos(x)

    f'(x) = cos(x) + 4 sin(x)

    If f(x) = tan(x) - 4/sec(x)
    then
    f(x) = tan(x) - 4 cos(x)
    f'(x) = sec2(x) + 4 sin(x)

  • Calculus -

    cos(x) + 4 sin(x) is correct. How did the 4 end up with the sin and not with the cos?

  • Calculus -

    It comes from
    -4/sec(x) = -4 cos(x)
    So when differentiated, it gives 4 sin(x)

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