derivative of 3x^2ln(x+x^2)

解

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

6 x ln (x) + 5 x

解答ステップ

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

和/差の法則を適用:

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

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

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

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

= 3 (2 x ln (x) + x) + 2 x

簡素化

3 (2 x ln (x) + x) + 2 x : 6 x ln (x) + 5 x

= 6 x ln (x) + 5 x