Derivatives of Inverse Trig Functions – PowerPoint

Recognise the derivatives of the standard inverse trigonometric functions

State the inverse function theorem and use it to differentiate the inverse of a given function

Derive the arcsine and arccosine derivatives from the definition of each inverse and the Pythagorean identity

The two recap slides on differentiation rules and trig derivatives come before any new content, so they can be shown or skipped depending on how recently the class met them

Three warm-up applications of the inverse function theorem sit between the theorem and the inverse trig work, which makes them the natural pause point in a lesson

The title slide carries a date field that displays the day the deck is opened, so check what it shows before projecting

Applying the inverse function theorem - three slides work it on ordinary functions, using the quotient rule and the chain rule, before it is used on any inverse trig function.

Deriving the arcsine derivative - the deck moves from the definition of inverse sine to cos(sin⁻¹x), then uses the Pythagorean identity to reach a form students can actually use.

Deriving the arccosine derivative - the same route is repeated with −sin(cos⁻¹x), which lets the sign difference emerge from the working rather than being asserted.