What is the first d/(dt)(3/t) ?

The first d/(dt)(3/t) is -3/(t^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

d/(dt)(3/t)

\frac{d}{d t} (\frac{3}{t})

- \frac{3}{t ^{2}}

Solution steps

\frac{d}{d t} (\frac{3}{t})

Take the constant out:

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

= 3 \frac{d}{d t} (\frac{1}{t})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 3 \frac{d}{d t} (t^{- 1})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 3 (- 1 \cdot t^{- 1 - 1})

Simplify

3 (- 1 \cdot t^{- 1 - 1}) : - \frac{3}{t ^{2}}

= - \frac{3}{t ^{2}}