展开 sqrt(a^2+(x+Δx)^2)-sqrt(a^2+x^2)

解答

展开

a^{2} + (x + Δ x)^{2} - a^{2} + x^{2}

a^{2} + x^{2} + 2Δ x^{2} + Δ^{2} x^{2} - a^{2} + x^{2}

求解步骤

a^{2} + (x + Δ x)^{2} - a^{2} + x^{2}

乘开

a^{2} + (x + Δ x)^{2} : a^{2} + x^{2} + 2Δ x^{2} + Δ^{2} x^{2}

= x^{2} + 2Δ x^{2} + Δ^{2} x^{2} + a^{2} - x^{2} + a^{2}

e x p an d y (y^{2} + 1) d x + x (y^{2} - 1) ln (x) d y

e x p an d (x - 1)^{3} (\frac{1}{x} + x)^{6}

s im pl i f y (x - \frac{1}{x ^{2}}) \cdot (x + \frac{1}{x ^{2}})

e x p an d cos (2 x^{3} - 9 x) (6 x^{2} - 9)

e x p an d - 2 (2 + 3) 2 - 3