derivative of 3x^4-16x^3+18x^2

解答

\frac{d}{d x} (3 x^{4} - 16 x^{3} + 18 x^{2})

12 x^{3} - 48 x^{2} + 36 x

求解步骤

\frac{d}{d x} (3 x^{4} - 16 x^{3} + 18 x^{2})

使用微分加减法定则:

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

= \frac{d}{d x} (3 x^{4}) - \frac{d}{d x} (16 x^{3}) + \frac{d}{d x} (18 x^{2})

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

\frac{d}{d x} (16 x^{3}) = 48 x^{2}

\frac{d}{d x} (18 x^{2}) = 36 x

= 12 x^{3} - 48 x^{2} + 36 x