derivative of (x-y^3^2-x^3)

解答

\frac{d}{d x} ((x - y^{3})^{2} - x^{3})

2 (x - y^{3}) (1 - 3 y^{2} \frac{d y}{d x}) - 3 x^{2}

求解步骤

\frac{d}{d x} ((x - y^{3})^{2} - x^{3})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} ((x - y^{3})^{2}) - \frac{d}{d x} (x^{3})

\frac{d}{d x} ((x - y^{3})^{2}) = 2 (x - y^{3}) (1 - 3 y^{2} \frac{d y}{d x})

\frac{d}{d x} (x^{3}) = 3 x^{2}

= 2 (x - y^{3}) (1 - 3 y^{2} \frac{d y}{d x}) - 3 x^{2}

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

e x p an d \frac{x ^{2} + 5 x - 1}{( x ^{2} + 3 ) ^{2}}

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

e x p an d \frac{( - 3 s ^{2} - 16 s + 12 )}{( s ^{2} + 4 ) ( s + 1 ) ( s - 4 )}

e x p an d P (s) a sc a l^{'} s