Derivatives of Inverse Trigonometric Functions

6. Derivatives of Inverse, Exponential, & Logarithmic Functions / Derivatives of Inverse Trigonometric Functions / Problem 3

Problem 3

Without finding the derivative of $y = \cos^{- 1} x$ , determine the slope of the line tangent to $y = \cos^{- 1} x$ at $open paren one half comma pi over 3 close paren$ .

$- 2 \sqrt{3}$

$- \frac{2 \sqrt{3}}{3}$

$the square root of 2$

$- \frac{\sqrt{2}}{2}$

Without finding the derivative of y=cos−1xy=\cos^{-1}x, determine the slope of the line tangent to y=cos−1xy=\cos^{-1}x at (12,π3)\left(\frac12,\frac{\pi}{3}\right).