展开 ((L+d-x))/(((L+d-x)^2+h^2)^{3/2)}

解答

展开

\frac{( L + d - x )}{( ( L + d - x ) ^{2} + h ^{2} ) ^{\frac{3}{2}}}

\frac{L}{( 2 d L - 2 Lx + L ^{2} + d ^{2} - 2 d x + x ^{2} + h ^{2} ) ^{\frac{3}{2}}} + \frac{d}{( 2 d L - 2 Lx + L ^{2} + d ^{2} - 2 d x + x ^{2} + h ^{2} ) ^{\frac{3}{2}}} - \frac{x}{( 2 d L - 2 Lx + L ^{2} + d ^{2} - 2 d x + x ^{2} + h ^{2} ) ^{\frac{3}{2}}}

求解步骤

\frac{L + d - x}{( ( L + d - x ) ^{2} + h ^{2} ) ^{\frac{3}{2}}}

((L + d - x)^{2} + h^{2})^{\frac{3}{2}} = (2 d L - 2 Lx + L^{2} + d^{2} - 2 d x + x^{2} + h^{2})^{\frac{3}{2}}

= \frac{L + d - x}{( 2 d L - 2 Lx + L ^{2} + d ^{2} - 2 d x + x ^{2} + h ^{2} ) ^{\frac{3}{2}}}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{L + d - x}{( 2 d L - 2 Lx + L ^{2} + d ^{2} - 2 d x + x ^{2} + h ^{2} ) ^{\frac{3}{2}}} = \frac{L}{( 2 d L - 2 Lx + L ^{2} + d ^{2} - 2 d x + x ^{2} + h ^{2} ) ^{\frac{3}{2}}} + \frac{d}{( 2 d L - 2 Lx + L ^{2} + d ^{2} - 2 d x + x ^{2} + h ^{2} ) ^{\frac{3}{2}}} - \frac{x}{( 2 d L - 2 Lx + L ^{2} + d ^{2} - 2 d x + x ^{2} + h ^{2} ) ^{\frac{3}{2}}}

= \frac{L}{( L ^{2} + 2 d L - 2 Lx + d ^{2} + x ^{2} + h ^{2} - 2 d x ) ^{\frac{3}{2}}} + \frac{d}{( L ^{2} + 2 d L - 2 Lx + d ^{2} + x ^{2} + h ^{2} - 2 d x ) ^{\frac{3}{2}}} - \frac{x}{( L ^{2} + 2 d L - 2 Lx + d ^{2} + x ^{2} + h ^{2} - 2 d x ) ^{\frac{3}{2}}}

\frac{d ^{2}}{d x ^{2}} ((y) (4 (2 x + 2) sin (x^{2} + 2 x + \frac{π}{2})))

e x p an d 3 + 0 (x - 1)

e x p an d \frac{- 2 ( 0 ) + 9}{- ( 0 ) ^{2} + 9}

e x p an d dd x (e^{x^{4}} + ln (5) (π))

e x p an d \frac{2}{( s + 1 ) ( s ^{2} + 4 )}