Odpowiedzi

2009-12-28T00:25:12+01:00
2009-12-28T00:58:11+01:00
1.
y=(x²+1)/(x²+2)
y'= [(x²+1)*(x²+2)' - (x²+1)' *(x²+2)] / (x²+2)²
y'= [(x²+1)*2x - 2x(x²+1)] / (x²+2)²
y'= 2x[(x²+1)-(x²+1)] / (x⁴+4x²+4)
y'= 2x/(x⁴+4x²+4)

3.
y=(x-1)² * (x+1)
y'= [(x-1)²]' * (x+1) + (x-1)² * (x+1)'
y'= 2(x-1)(x+1) + (x-1)² * 1
y'=2(x²-1) + (x-1)²
y'=2x²-2 + x²-2x+1
y'=3x²-2x-1

4.
y=(√x +1)/(√x +2)
y'= [(√x+1)' * (√x+2) - (√x +1)*(√x+2)']/(√x+2)²
y'= {[½x ^ (-½) ]*(√x+2) - (√x +1)*[½x ^ (-½)]} / x+4√x +4
y'= [½ * (1/√x)(√x+2) - (√x+1)*½*(1/√x)] / x+4√x+4
y'= {(√x+2)/(2√x)] - [(√x+1)/√x]} / x+4√x+4

6.
y=3/ (1-x²)(1-2x³)
y'= 3' * (1-x²)(1-2x³) - 3 * (1-x²)(1-2x³)'
y'=0 - 3* [(1-x²)'(1-2x³) + (1-x²) *(1-2x³)']
y'= -3*[-2x(1-2x³) + (1-x²)*(-6x²)]
y'= 6x(1-2x³) +18x²(1-x²)
y'= 6x-12x⁴+18x²-18x⁴
y'= -30x⁴+18x²+6x

7.
y=(x+1)/(x²-2)
y'= [(x+1)' *(x²-2) - (x+1)* (x²-2)' ] / (x²-2)²
y'= [1*(x²-2) - (x+1)*2x] / (x⁴-4x² +4)
y'= (x²-2 - 2x²+2x) / (x⁴-4x²+4)
y'= (-x²+2x-2) / (x⁴-4x²+4)
2009-12-28T06:36:02+01:00
1.
y = (x² + 1) / (x² + 2)
y' = [(x² + 1)' * (x² + 2) - (x² + 2)' * (x² + 1)] / (x² + 2)²
y' = [2x(x² + 2) - 2x(x² + 1)] / (x² + 2)²
y' = 2x[x² + 2 - x² - 1)] / (x² + 2)²
y' = 2x/(x² + 2)²

3.
y = (x - 1)² * (x + 1)
y' = [(x - 1)²]' * (x + 1) + (x - 1)²(x + 1)'
y' = 2(x - 1)(x + 1) + (x - 1)² * 1
y' = 2(x² - 1) + (x - 1)²
y' = 2x² - 2 + x² - 2x + 1
y' = 3x² - 2x - 1

4.
y = (√x + 1) / (√x + 2)
y' = [(√x + 1)' * (√x + 2) - (√x + 1) * (√x + 2)'] / (√x + 2)²
y' = [1/2√x * (√x + 2) - (√x + 1) * 1/2√x] / (√x + 2)²
y' = [1/2√x(√x + 2 - √x - 1) / (√x + 2)²
y' = 1/2√x / (√x + 2)²
y' = 1 / [2√x(√x + 2)²]

6.
y = 3 / (1 - x²)(1 - 2x³)
y'= {3' * (1 - x²)(1 - 2x³) - 3[(1-x²)(1-2x³)]'} / [(1 - x²)(1 - 2x³)]²
y'; = {- 3[(1 - x²)'(1 - 2x³) + (1 - x²)(1 - 2x³)']} / [(1 - x²)(1 - 2x³)]²
y' = {- 3[- 2x(1 - 2x³) + (1 - x²)(- 6x²)]} / [(1 - x²)(1 - 2x³)]²
y' = [- 3 * (- 2x + 4x⁴ - 6x² + 6x⁴)] / [(1 - x²)(1 - 2x³)]²
y' = [- 3 * (10x⁴ - 6x² - 2x)] / [(1 - x²)(1 - 2x³)]²
y' = (- 30x⁴ + 18x² + 6x) / [(1 - x²)(1 - 2x³)]²

7.
y = (x + 1) /(x² - 2)
y' = [(x + 1)' *(x² - 2) - (x + 1)* (x² - 2)'] / (x² - 2)²
y' = [1 * (x² - 2) - (x + 1) * 2x] / (x² - 2)²
y' = (x² - 2 - 2x² - 2x) / (x² - 2)²
y' = (- x² - 2x - 2) / (x² - 2)²
y' = -(x² + 2x + 2) / (x² - 2)²