What is the first d/(dθ)(1/θ) ?

The first d/(dθ)(1/θ) is -1/(θ^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

d/(dθ)(1/θ)

\frac{d}{d θ} (\frac{1}{θ})

- \frac{1}{θ ^{2}}

Solution steps

\frac{d}{d θ} (\frac{1}{θ})

Apply exponent rule:

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

= \frac{d}{d θ} (θ^{- 1})

Apply the Power Rule:

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

= - 1 \cdot θ^{- 1 - 1}

Simplify

- 1 \cdot θ^{- 1 - 1} : - \frac{1}{θ ^{2}}

= - \frac{1}{θ ^{2}}