Derivatives of Inverse Trig Functions

Example: Find the derivative of: y(x) = sin^-1(2x²) .

Strategy to calcuate derivatives of inverse trig functions

Define a new variable, w, where w = sin^-1(2x²)

Then sin w = 2x². Now take the derivative with respect to x on both sides.

cos w dw/dx = 4x so the derivative of the inverse function is

dw/dx = 4x (sec w)

Since sin w = 2 x² Construct the following diagram to find sec w.

From the above diagram sec w = [ 1/ √ (1 ˗ 4 x⁴ ) ]

So the derivative of y(x) = 4x [ 1/ √(1 ˗ 4 x⁴ ) ] (result)

Return to Notes for Calculus 1

Copyright © 2019 Richard C. Coddington

All rights reserved.