Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises - Page 122: 21

$f’(x) = 1$

$f(x) = (x^{\frac{1}{2}}+1)(x^{\frac{1}{2}}-1); $ $ x\geq 0 $ Product and Power Rules: $f’(x) = \frac{1}{2}( x^{-\frac{1}{2}})(x^{\frac{1}{2}}-1) + \frac{1}{2}( x^{-\frac{1}{2}})(x^{\frac{1}{2}}+1) $ $f’(x) = \frac{1}{2} (1-x^{-\frac{1}{2}}) + \frac{1}{2}(1+ x^{-\frac{1}{2}}) $ $f’(x) = \frac{1}{2} (1-x^{-\frac{1}{2}} + 1+ x^{-\frac{1}{2}}) $ $f’(x) = \frac{1}{2} (2) $ $f’(x) = 1 $