d/(dt)(sin(3ln(t)-e^{t^2}))

解

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

cos (3 ln (t) - e^{t^{2}}) (\frac{3}{t} - e^{t^{2}} \cdot 2 t)

解答ステップ

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

連鎖法則を適用:

cos (3 ln (t) - e^{t^{2}}) \frac{d}{d t} (3 ln (t) - e^{t^{2}})

= cos (3 ln (t) - e^{t^{2}}) \frac{d}{d t} (3 ln (t) - e^{t^{2}})

\frac{d}{d t} (3 ln (t) - e^{t^{2}}) = \frac{3}{t} - e^{t^{2}} \cdot 2 t

= cos (3 ln (t) - e^{t^{2}}) (\frac{3}{t} - e^{t^{2}} \cdot 2 t)