Chapter 2 - The Derivative - 2.6 The Chain Rule - Exercises Set 2.6 - Page 158: 26

$$f'(x)=-4(x^4-\sec(4x^2-2))^{-5}(4x^3-8x\sec(4x^2-2)\tan(4x^2-2))$$

$$f'(x)=\Big((x^4-\sec(4x^2-2))^{-4}\Big)'=-4(x^4-\sec(4x^2-2))^{-5}\cdot(x^4-\sec(4x^2-2))'= -4(x^4-\sec(4x^2-2))^{-5}(4x^3-\sec(4x^2-2)\tan(4x^2-2)\cdot(4x^2-2)')= -4(x^4-\sec(4x^2-2))^{-5}(4x^3-\sec(4x^2-2)\tan(4x^2-2)\cdot8x)= -4(x^4-\sec(4x^2-2))^{-5}(4x^3-8x\sec(4x^2-2)\tan(4x^2-2))$$