Question

Помогите решить 4.3 и 4.14 даю 35 баллов

Answer 1

$4.3)\; \; y=(1+x^4)^{tg7x}\\\\lny=ln(1+x^4)^{tg7x}\\\\lny=tg7x\cdot ln(1+x^4)\\\\(lny)'=(tg7x\cdot ln(1+x^4))'\\\\\frac{y'}{y}=7\cdot \frac{1}{cos^27x}\cdot ln(1+x^4)+tg7x\cdot \frac{4x^3}{1+x^4}\\\\y'=y\cdot \Big ( \frac{7}{cos^27x}\cdot ln(1+x^4)+tg7x\cdot \frac{4x^3}{1+x^4}\Big )\\\\y'=(1+x^4)^{tg7x}\cdot \Big (\frac{7\cdot ln(1+x^4)}{cos^27x} +\frac{4x^3\cdot tg7x}{1+x^4}\Big )$

$4.14)\; \; y=(\sqrt{x+5})^{ln\frac{3}{x}}\\\\lny=ln \frac{3}{x} \cdot ln\sqrt{x+5}\\\\\frac{y'}{y}=\frac{x}{3}\cdot \frac{-3}{x^2}\cdot ln\sqrt{x+5}+ln \frac{3}{x}\cdot \frac{1}{\sqrt{x+5}} \cdot \frac{1}{2\sqrt{x+5}}\\\\y'=(\sqrt{x+5})^{ln\frac{3}{x}}\cdot \Big (-\frac{1}{x}\cdot ln\sqrt{x+5}+ln \frac{3}{x} \cdot \frac{1}{2(x+5)}\Big )$