展开 y(d^2)/(d^2x)(y^2=x^2+2x)

解答

展开

y \frac{d ^{2}}{d ^{2} x} (y^{2} = x^{2} + 2 x)

\frac{y ^{3}}{x} = x^{2} + 2 y

求解步骤

y \frac{d ^{2}}{d ^{2} x} (y^{2} = x^{2} + 2 x)

= \frac{d ^{2}}{d ^{2} x} y (= x^{2} y^{2} + 2 x)

使用分配律:

a (b + c) = ab + a c

a = y \frac{d ^{2}}{d ^{2} x}, b = y^{2} = x^{2}, c = 2 x

y \frac{d ^{2}}{d ^{2} x} y^{2} = x^{2} + y \frac{d ^{2}}{d ^{2} x} \cdot 2 x

\frac{d ^{2}}{d ^{2} x} y y^{2} = x^{2} + 2 \cdot \frac{d ^{2}}{d ^{2} x} x y

化简

\frac{d ^{2}}{d ^{2} x} y y^{2} = x^{2} + 2 \cdot \frac{d ^{2}}{d ^{2} x} x y : \frac{y ^{3}}{x} = x^{2} + 2 y

\frac{y ^{3}}{x} = x^{2} + 2 y

e x p an d \frac{1}{( t ^{4} + 1 ) ^{3}}

e x p an d \frac{4 y ( x + 2 ) - 6}{( x + 2 ) ^{2}}

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

e x p an d \frac{2 ( 715 - p ) ^{2}}{5}

e x p an d \frac{a ^{2} + b ^{2} + c ^{2} + 3 ab c}{( a + b ) ( b + c ) ( c + a )}