derivative of x^4-4x^3+3x^2-3

解答

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

4 x^{3} - 12 x^{2} + 6 x

求解步骤

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

使用微分加减法定则:

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

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

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

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

\frac{d}{d x} (3 x^{2}) = 6 x

\frac{d}{d x} (3) = 0

= 4 x^{3} - 12 x^{2} + 6 x - 0

化简

= 4 x^{3} - 12 x^{2} + 6 x

\int (x^{2} - 2 x + 5) e^{- x} d x

x \to - 2 lim (7 x^{2} + 8)

d er i v a t i v e cos (- 3 x)

d er i v a t i v e sin (t) - sin (t) cos (t) - 5 t

d er i v a t i v e f (t) = - \frac{50}{t ^{3}} + \frac{5}{t ^{2}}