derivative t^{sqrt(13t)}

解

導関数

t^{13 t}

13 t^{13 t} (\frac{ln ( t )}{2 t} + \frac{1}{t})

解答ステップ

\frac{d}{d t} (t^{13 t})

簡素化

t^{13 t} : t^{13 t}

= \frac{d}{d t} (t^{13 t})

指数の規則を適用する:

a^{b} = e^{b l n (a)}

t^{13 t} = e^{13 t l n (t)}

= \frac{d}{d t} (e^{13 t l n (t)})

連鎖法則を適用:

e^{13 t l n (t)} \frac{d}{d t} (13 t ln (t))

= e^{13 t l n (t)} \frac{d}{d t} (13 t ln (t))

\frac{d}{d t} (13 t ln (t)) = 13 (\frac{ln ( t )}{2 t} + \frac{1}{t})

= e^{13 t l n (t)} 13 (\frac{ln ( t )}{2 t} + \frac{1}{t})

e^{13 t l n (t)} = t^{13 t}

= 13 t^{13 t} (\frac{ln ( t )}{2 t} + \frac{1}{t})