derivative 5tln(t)

解答

导数

5 t ln (t)

5 (ln (t) + 1)

求解步骤

\frac{d}{d t} (5 t ln (t))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d t} (t ln (t))

使用微分乘法定则:

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

f = t, g = ln (t)

= 5 (\frac{d t}{d t} ln (t) + \frac{d}{d t} (ln (t)) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (ln (t)) = \frac{1}{t}

= 5 (1 \cdot ln (t) + \frac{1}{t} t)

化简

5 (1 \cdot ln (t) + \frac{1}{t} t) : 5 (ln (t) + 1)

= 5 (ln (t) + 1)

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