Aplicando a definição, encontrar a função derivada da função y = (x+20)/x2
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Lim (x+h +20)/(x+h)² -(x+20)/x²
h-->0 -------------------------------------
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Lim [(x+h +20)x² -(x+20)(x+h)²]/x²(x+h)²
h-->0 -------------------------------------
h
Lim [(x+h +20)x² -(x+20)(x²+2xh+h²)]/x²(x+h)²
h-->0 ---------------------------------------------------------
h
Lim [x³+hx²+20x²-x³-2x²h-xh²-20x²-40xh-20h² ]/x²(x+h)²
h-->0 -----------------------------------------------------------------
h
Lim [hx²-2x²h-xh²-40xh-20h² ]/x²(x+h)²
h-->0 ---------------------------------------------
h
Lim [x²-2x²-xh-40x-20h ]/x²(x+h)²
h-->0
[x²-2x²-40x ]/x²(x)² = (-x²-40x)/x⁴ =(-x-40)/x³
h-->0 -------------------------------------
h
Lim [(x+h +20)x² -(x+20)(x+h)²]/x²(x+h)²
h-->0 -------------------------------------
h
Lim [(x+h +20)x² -(x+20)(x²+2xh+h²)]/x²(x+h)²
h-->0 ---------------------------------------------------------
h
Lim [x³+hx²+20x²-x³-2x²h-xh²-20x²-40xh-20h² ]/x²(x+h)²
h-->0 -----------------------------------------------------------------
h
Lim [hx²-2x²h-xh²-40xh-20h² ]/x²(x+h)²
h-->0 ---------------------------------------------
h
Lim [x²-2x²-xh-40x-20h ]/x²(x+h)²
h-->0
[x²-2x²-40x ]/x²(x)² = (-x²-40x)/x⁴ =(-x-40)/x³
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