derivative of 3x^4-5x^2+2sqrt(3x)

解

\frac{d}{d x} (3 x^{4} - 5 x^{2} + 2 3 x)

12 x^{3} - 10 x + \frac{3}{x}

解答ステップ

\frac{d}{d x} (3 x^{4} - 5 x^{2} + 2 3 x)

簡素化

3 x^{4} - 5 x^{2} + 2 3 x : 3 x^{4} - 5 x^{2} + 23 x

= \frac{d}{d x} (3 x^{4} - 5 x^{2} + 23 x)

和/差の法則を適用:

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

= \frac{d}{d x} (3 x^{4}) - \frac{d}{d x} (5 x^{2}) + \frac{d}{d x} (23 x)

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

\frac{d}{d x} (5 x^{2}) = 10 x

\frac{d}{d x} (23 x) = \frac{3}{x}

= 12 x^{3} - 10 x + \frac{3}{x}