(d^2)/(dx^2)(((x+b)(x-a))/((x-b)))

解

\frac{d ^{2}}{d x ^{2}} (\frac{( x + b ) ( x - a )}{( x - b )})

\frac{4 b ( b - a )}{( x - b ) ^{3}}

解答ステップ

\frac{d ^{2}}{d x ^{2}} (\frac{( x + b ) ( x - a )}{( x - b )})

\frac{d}{d x} (\frac{( x + b ) ( x - a )}{x - b}) = \frac{x ^{2} - 2 b x - b ^{2} + 2 ba}{( x - b ) ^{2}}

= \frac{d}{d x} (\frac{x ^{2} - 2 b x - b ^{2} + 2 ba}{( x - b ) ^{2}})

\frac{d}{d x} (\frac{x ^{2} - 2 b x - b ^{2} + 2 ba}{( x - b ) ^{2}}) = \frac{4 b ( b - a )}{( x - b ) ^{3}}

= \frac{4 b ( b - a )}{( x - b ) ^{3}}