Question

Найти производную функции. 1)y=5sin(3x^2-2) 2)y=ln(x^2-2) 3)y=e^x^2+5x 4)y=2cos(x^5-3)

Answer 1

$1)\; \; y=5sin(3x^2-2)\\\\y'=5\cdot cos(3x^2-2)\cdot 6x\\\\2)\; \; y=ln(x^2-2)\\\\y'= \frac{1}{x^2-2} \cdot 2x\\\\3)\; \; y=e^{x^2}+5x\\\\y'=e^{x^2}\cdot 10x+5\\\\\Big (\; y=e^{x^2+5x}\; \; \to \; \; \; y'=e^{x^2+5x}\cdot (2x+5)\; \Big )\\\\4)\; \; y=2cos(x^5-3)\\\\y'=-2sin(x^5-3)\cdot 5x^4$