Question

Памагити. Найти производную в примерах г, е и ж

Answer 1

$1)\; \; y=(x^6-\frac{2}{x^3}-7)^3\\\\y'=3\cdot (x^6-\frac{2}{x^3}-7)^2\cdot (6x^5-\frac{-2\cdot 3x^2}{x^6})=3\cdot (x^6-\frac{2}{x^3}-7)^3\cdot (6x^5+\frac{6}{x^4})\\\\2)\; \; y=4^{arctgx}\cdot sin5x\\\\y'=4^{arctgx}\cdot ln4\cdot sin5x+4^{arctgx}\cdot 5\, cos5x\\\\3)\; \; x^2y^3+x\cdot lny=0\; \; ,\; \; [\, y=y(x)\; -\; fynkciya\, ]\\\\2x\cdot y^3+x^2\cdot 3y^2y'+lny+x\cdot \frac{y'}{y}=0\\\\y'\cdot (3x^2y^2+\frac{x}{y})=-(2xy^3+lny)\\\\y'\cdot \frac{3x^2y^3+x}{y}=-(2xy^3+lny)\\\\y'=-\frac{y\cdot (2xy^3+lnx)}{x\cdot (3xy^3+1)}$