derivative of 5*T{g}(T,x(2x^3)+2/(x^2))

解

\frac{d}{d x} (5 \cdot T g (T, x) (2 x^{3}) + \frac{2}{x ^{2}})

5 T \cdot 2 (\frac{d}{d x} (g (T, x)) x^{3} + 3 x^{2} g (T, x)) - \frac{4}{x ^{3}}

解答ステップ

\frac{d}{d x} (5 T g (T, x) (2 x^{3}) + \frac{2}{x ^{2}})

T

を定数として扱う

和/差の法則を適用:

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

= \frac{d}{d x} (5 T g (T, x) \cdot 2 x^{3}) + \frac{d}{d x} (\frac{2}{x ^{2}})

\frac{d}{d x} (5 T g (T, x) \cdot 2 x^{3}) = 5 T \cdot 2 (\frac{d}{d x} (g (T, x)) x^{3} + 3 x^{2} g (T, x))

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

= 5 T \cdot 2 (\frac{d}{d x} (g (T, x)) x^{3} + 3 x^{2} g (T, x)) - \frac{4}{x ^{3}}