Inverse trigometric derivatives are exactly what they sound like: derivatives of inverse trigometric functions. Each function has a specific term as its derivative. They are as follows...
It looks like chaos, but it's actually pretty simple. The u in each represents whatever is inside the function. After the u has been plugged into the fraction, you must multiply the fraction by the DERIVATIVE of u. That's really all that is unique to inverse trig functions. In order to finish solving, you must employ other derivative techniques such as product rules and quotient rules .
Note: 1/sin is NOT the same as Sin -1 . When taking the derivative of an inverse function, do not keep the function when writing the fraction. (eg: Do not write "Csc-1 " in the derivative)
Note: 1/sin is NOT the same as Sin -1 . When taking the derivative of an inverse function, do not keep the function when writing the fraction. (eg: Do not write "Csc-1 " in the derivative)
Examples: Differentiate the following.
Answers can be found here