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Derivatives of Inverse Trig Functions

Learn how to find derivatives of inverse trigonometric functions at x = 2 and x = 4 using reciprocal slopes and derivative formulas. Understand the pattern and use implicit differentiation to solve related problems.

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Derivatives of Inverse Trig Functions

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  1. Photo by Vickie Kelly, 1993 Greg Kelly, Hanford High School, Richland, Washington Derivatives of Inverse Trig Functions

  2. At x = 2: We can find the inverse function as follows: To find the derivative of the inverse function: Switch x and y.

  3. Slopes are reciprocals. At x = 2: At x = 4:

  4. Slopes are reciprocals. The derivative of Derivative Formula for Inverses: evaluated at the derivative of evaluated at . Because x and y are reversed to find the reciprocal function, the following pattern always holds: is equal to the reciprocal of

  5. Given: Find: Derivative Formula for Inverses: A typical problem using this formula might look like this:

  6. We can use implicit differentiation to find:

  7. But so is positive. We can use implicit differentiation to find:

  8. We could use the same technique to find and . d - 1 sec x dx

  9. Your calculator contains all six inverse trig functions. However it is occasionally still useful to know the following: p

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