Question

Найти производные функций f(x)

Answer 1

$1)\; \; f(x)=\frac{sinx^2\cdot 2^{3x+4}}{\sqrt{6x-8}}\\\\y'=\frac{1}{6x-8}\cdot \Big ((2x\cdot cosx^2\cdot 2^{3x+4}+sinx^2\cdot 2^{3x+4}\cdot 3)\cdot \sqrt{6x-8}-\\\\-sinx^2\cdot 2^{3x+4}\cdot \frac{1}{2\sqrt{6x-8}}\cdot 6\Big )\\\\\\2)\; \; y=(4x^3-6)^{2x}\\\\lny=ln(4x^3-6)^{2x}\\\\lny=2x\cdot ln(4x^3-6)\\\\\frac{y'}{y}=2\cdot ln(4x^3-6)+2x\cdot \frac{1}{4x^3-6}\cdot 12x^2\\\\y'=(4x^3-6)^{2x}\cdot \Big (2\cdot ln(4x^3-6)+\frac{24x^3}{4x^3-6}\Big )$