derivative of 12x^5+45x^4-200x^3+4

解答

\frac{d}{d x} (12 x^{5} + 45 x^{4} - 200 x^{3} + 4)

60 x^{4} + 180 x^{3} - 600 x^{2}

求解步骤

\frac{d}{d x} (12 x^{5} + 45 x^{4} - 200 x^{3} + 4)

使用微分加减法定则:

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

= \frac{d}{d x} (12 x^{5}) + \frac{d}{d x} (45 x^{4}) - \frac{d}{d x} (200 x^{3}) + \frac{d}{d x} (4)

\frac{d}{d x} (12 x^{5}) = 60 x^{4}

\frac{d}{d x} (45 x^{4}) = 180 x^{3}

\frac{d}{d x} (200 x^{3}) = 600 x^{2}

\frac{d}{d x} (4) = 0

= 60 x^{4} + 180 x^{3} - 600 x^{2} + 0

化简

= 60 x^{4} + 180 x^{3} - 600 x^{2}

a re a y = x^{2} - 2, y = x

\frac{d}{d x} (7 x^{2})

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

x^{^{''}} + 100 x = 0

\int \frac{1}{4 x - 1} d x