derivative sin(t^2)ln(t^3)

解

導関数

sin (t^{2}) ln (t^{3})

2 t cos (t^{2}) ln (t^{3}) + \frac{3 sin ( t ^{2} )}{t}

解答ステップ

\frac{d}{d t} (sin (t^{2}) ln (t^{3}))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (t^{2}), g = ln (t^{3})

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

\frac{d}{d t} (sin (t^{2})) = cos (t^{2}) \cdot 2 t

\frac{d}{d t} (ln (t^{3})) = \frac{3}{t}

= cos (t^{2}) \cdot 2 t ln (t^{3}) + \frac{3}{t} sin (t^{2})

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 2 t cos (t^{2}) ln (t^{3}) + \frac{3 sin ( t ^{2} )}{t}