What is the derivative of 1/z ?

The derivative of 1/z is -1/(z^2)

What is the first derivative of 1/z ?

The first derivative of 1/z is -1/(z^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{1}{z}

- \frac{1}{z ^{2}}

Solution steps

\frac{d}{d z} (\frac{1}{z})

Apply exponent rule:

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

= \frac{d}{d z} (z^{- 1})

Apply the Power Rule:

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

= - 1 \cdot z^{- 1 - 1}

Simplify

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

= - \frac{1}{z ^{2}}

\int (3 x^{2} - 2 x + 5) d x

f (x) = - \frac{3}{x}

y^{^{''}} - 5 y^{^{'}} + 6 y = cos (x) e^{- x}

\int \frac{sin ( 2 x )}{32 + cos ^{2} ( x )} d x

\frac{d P}{d t} = 0.16 P (1 - \frac{P}{1000}) - 30, P (0) = 200