展开 1/2 ((9-a^2)/2+1/2 (1/(e^6)-e^{-2a}))

解答

展开

\frac{1}{2} (\frac{9 - a ^{2}}{2} + \frac{1}{2} (\frac{1}{e ^{6}} - e^{- 2 a}))

- \frac{1}{4} e^{- 2 a} + \frac{9}{4} + \frac{1}{4 e ^{6}} - \frac{a ^{2}}{4}

求解步骤

\frac{1}{2} (\frac{9 - a ^{2}}{2} + \frac{1}{2} (\frac{1}{e ^{6}} - e^{- 2 a}))

使用分配律:

a (b + c) = ab + a c

a = \frac{1}{2}, b = \frac{9 - a ^{2}}{2}, c = \frac{1}{2} (\frac{1}{e ^{6}} - e^{- 2 a})

= \frac{1}{2} \cdot \frac{9 - a ^{2}}{2} + \frac{1}{2} \cdot \frac{1}{2} (\frac{1}{e ^{6}} - e^{- 2 a})

化简

\frac{1}{2} \cdot \frac{9 - a ^{2}}{2} + \frac{1}{2} \cdot \frac{1}{2} (\frac{1}{e ^{6}} - e^{- 2 a}) : - \frac{1}{4} e^{- 2 a} + \frac{9}{4} + \frac{1}{4 e ^{6}} - \frac{a ^{2}}{4}

= - \frac{1}{4} e^{- 2 a} + \frac{9}{4} + \frac{1}{4 e ^{6}} - \frac{a ^{2}}{4}

e x p an d (x^{2} + 1) sec (h) (ln (x))

e x p an d 5 - 3 5 + 6

e x p an d \frac{d}{d x} ((x - 3) e^{x}) - (x + 1) e^{- x}

e x p an d \frac{c ( b + 4 )}{( c + d )}

e x p an d 5 (2.5)^{3} - 3 (2.5)^{2} - 6 (2.5) - 16