展开 5(x+Δx)^2+(x+Δx)+3

解答

展开

5 (x + Δ x)^{2} + (x + Δ x) + 3

5 x^{2} + 10Δ x^{2} + 5 Δ^{2} x^{2} + x + Δ x + 3

求解步骤

5 (x + Δ x)^{2} + (x + Δ x) + 3

去除括号:

(a) = a

= 5 (x + Δ x)^{2} + x + Δ x + 3

(x + Δ x)^{2} = x^{2} + 2Δ x^{2} + Δ^{2} x^{2}

= 5 (x^{2} + 2Δ x^{2} + Δ^{2} x^{2}) + x + Δ x + 3

乘开

5 (x^{2} + 2Δ x^{2} + Δ^{2} x^{2}) : 5 x^{2} + 10Δ x^{2} + 5 Δ^{2} x^{2}

= 5 x^{2} + 10Δ x^{2} + 5 Δ^{2} x^{2} + x + Δ x + 3

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

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e x p an d \frac{f ( x + h ) - x ^{2} - 1}{h}

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e x p an d (8 x^{2} - 2 x y + 3) d x