Notice the domain restrictions for inverse sine, cosine, secant, and cosecant.
Example 1: = sin−1 x^2 =
Example 2: = tan−1 5 x =
Example 3:
Finding the derivatives of inverse trig functions is just a matter of following the formulas. They’re very
rarely tested on the AP Exam in this form and are not terribly important. In addition, the AP Exam almost
always tests only inverse sine and tangent, and then usually only as integrals, not as derivatives.
Therefore, it’s time to learn the integrals. The derivative formulas lead directly to the integral formulas,
but because the only difference between the derivatives of inverse sine, tangent, and secant and those of
inverse cosine, cotangent, and cosecant is the negative sign, only the former functions are generally used.