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AP calculus BC

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i know that deriv(cscx) = -cscxcotx
and that
deriv(cos) = -sinx
deriv(cotx) = -((cscx)^2)
my question is:
is this (statements below) correct?
antideriv(cscxcotx) = -(cscx)
antideriv(sinx) = -cosx
antideriv((cscx)^2)= -cotx

were those antiderivatives above correct?
ALSO basically my question is how i can remember where the negative sign goes and with which trig funcation it goes with; also is this correct : to go from a derivative to an antiderivative, (visually) change the derivative symbol to an antiderivative symbol, then switch the places of the trig identities on either side of the equal sign (flipflop them), and keep the negative sign where it is....? is this right? thank you!

  • AP calculus BC -

    1. THey are right.
    2. How can you remember? Flash cards.
    3. I don't like that rule, complicated. I just recommend memorizing the derivatives, when that is done, the inverse operation is easy. Flash cards.

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