Question

Найти производные у " у' и у"' следущих функций
у=(1+х) * аrtgx

Answer 1

y`=arctgx+1/(1+x²)
y``=1/(1+x²) -2x/(1+x²)²
y```=-2x/(1+x²)² -[2(1+x²)²-2x*2(1+x²)*2x]/(1+x²)^4=
=-2x/(1+x²)² -(2+4x²+2x^4-8x²-8x^4)/(1+x²)^4=
=-2x/(1+x²)² -(2-4x²-6x^4)/(1+x²)^4