Chapter 3 - Determining Change: Derivatives - 3.5 Activities - Page 233: 14

(a)$f(x)=5e^{2x}(20x^3-30)$ (b)$f^{'}(x)=[10e^{2x}](20x^3-30)+5e^{2x} [60x^2] $

$g(x)=5e^{2x};h(x)=20x^3-30$ (a) Let $f(x)=g(x) h(x)$ $f(x)=5e^{2x}(20x^3-30)$ (b) Taking derivative of f(x) with respect to x, using product rule $f^{'}(x)=g^{'}(x)h(x)+g(x)h^{'}(x)$ $f^{'}(x)=[5(2)e^{2x}](20x^3-30)+5e^{2x} [20(3)x^2-0] $ $f^{'}(x)=[10e^{2x}](20x^3-30)+5e^{2x} [60x^2] $