Question

Buktikan bahwa :

jawab yaa teman teman yg baik hatinya :)

Answer 1

Kita pakai misal
y = y1 + y2 + y3
y1 = 3x² - 1 / 3x³
(y1)' = (6x(3x³) - 9x²(3x²-1)) / (9x^6)
     = (18 x^4 - 27x^4 + 9x² )/(9x^6)
   = (-9x^4 + 9x^2) / (9x^6)
   = 9x²(1 - x²)/(9x^6)
   = (1-x²) / (x^4)
y2 = ln √1+x²
(y2)' = x / √1 +x²
y3 = arctanx
(y3)' = 1 / (1 + x²)
(y2)' + (y3)' = x / √(1+x²)  + 1/(1+x²)
     = (x√(1+x²) + 1)/ (1+x²)
(y1)'+(y2)'+(y3)' = (1-x²)/ x^4  + x√(1+x²) +1 )(1+x²)
   = (1-x^4) + x^5√(1+x²) +x^4) / (x^4(1+x²)
   = (1 + x^5√(1+x²)) / (x^4 + x^6)

y' =