展开 (x-1)^2sin(1/(x-1))

解答

展开

(x - 1)^{2} sin (\frac{1}{x - 1})

sin (\frac{1}{x - 1}) x^{2} - 2 x sin (\frac{1}{x - 1}) + sin (\frac{1}{x - 1})

求解步骤

(x - 1)^{2} sin (\frac{1}{x - 1})

= sin (\frac{1}{x - 1}) (x - 1)^{2}

展开

(x - 1)^{2} : x^{2} - 2 x + 1

= sin (\frac{1}{x - 1}) (x^{2} - 2 x + 1)

使用分配律:

m (a + b + c) = ma + mb + m c

sin (\frac{1}{x - 1}) (x^{2} - 2 x + 1) = sin (\frac{1}{x - 1}) x^{2} + sin (\frac{1}{x - 1}) (- 2 x) + sin (\frac{1}{x - 1}) \cdot 1

= sin (\frac{1}{x - 1}) x^{2} + sin (\frac{1}{x - 1}) (- 2 x) + sin (\frac{1}{x - 1}) \cdot 1

sin (\frac{1}{x - 1}) (- 2 x) = - 2 x sin (\frac{1}{x - 1})

sin (\frac{1}{x - 1}) \cdot 1 = sin (\frac{1}{x - 1})

= sin (\frac{1}{x - 1}) x^{2} - 2 x sin (\frac{1}{x - 1}) + sin (\frac{1}{x - 1})

e x p an d \frac{( e ^{x} + e ^{- x} ) ^{2}}{4}

e x p an d \frac{8 x - 5}{( 4 x - 7 ) ^{2}}

e x p an d (\frac{4}{2 - 5 x})^{3}

e x p an d \frac{7 ( x + h ) ^{2}}{2}

e x p an d (cos (a) + cos (b)) (cos (a) - cos (b))