展开 y'(x)(2x+1)^3

解答

展开

y^{'} (x) (2 x + 1)^{3}

8 x^{3} y' (x) + 12 x^{2} y' (x) + 6 x y' (x) + y' (x)

求解步骤

y^{'} (x) (2 x + 1)^{3}

(2 x + 1)^{3} = 8 x^{3} + 12 x^{2} + 6 x + 1

= y^{^{'}} (x) (8 x^{3} + 12 x^{2} + 6 x + 1)

打开括号

= y^{^{'}} (x) 8 x^{3} + y^{^{'}} (x) 12 x^{2} + y^{^{'}} (x) 6 x + y^{^{'}} (x) 1

= 8 x^{3} y^{^{'}} (x) + 12 x^{2} y^{^{'}} (x) + 6 x y^{^{'}} (x) + 1 y^{^{'}} (x)

乘以:

1 y^{'} (x) = y^{'} (x)

= 8 x^{3} y^{^{'}} (x) + 12 x^{2} y^{^{'}} (x) + 6 x y^{^{'}} (x) + y^{^{'}} (x)

e x p an d \frac{1}{48} (x - 5) (x - 3)

s im pl i f y (10) \cdot (1 + (12 \cdot 1 0^{- 6} (\circ c)^{- 1})) \cdot (80)

e x p an d \frac{- ln ( 5 + e ) + 2}{ln ^{3} ( 5 + e ) ( 5 + e )}

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

e x p an d 2 (2 x + 2 y = - 4)