derivative 4x^3-56x^2+196x

解答

导数

4 x^{3} - 56 x^{2} + 196 x

12 x^{2} - 112 x + 196

求解步骤

\frac{d}{d x} (4 x^{3} - 56 x^{2} + 196 x)

使用微分加减法定则:

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

= \frac{d}{d x} (4 x^{3}) - \frac{d}{d x} (56 x^{2}) + \frac{d}{d x} (196 x)

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (56 x^{2}) = 112 x

\frac{d}{d x} (196 x) = 196

= 12 x^{2} - 112 x + 196

\int \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} d x

\int 2 x^{3} e^{- 2 x} d x

x \to \frac{π}{4} lim (\frac{cos ( 2 x )}{2 cos ( x ) - 1})

cos^{2} (x) sin (x) d y + (y cos^{3} (x) - 1) d x = 0

x^{2} \frac{d y}{d x} + 2 x y = 5 y^{3}