What is the derivative of y= 1/(f(x)) ?

The derivative of y= 1/(f(x)) is -(\frac{df)/(dx)}{f(x)^2}

What is the first derivative of y= 1/(f(x)) ?

The first derivative of y= 1/(f(x)) is -(\frac{df)/(dx)}{f(x)^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = \frac{1}{f ( x )}

- \frac{\frac{df}{d x}}{f ( x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{f ( x )})

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{f ( x ) ^{2}} \frac{df}{d x}

= - \frac{1}{f ( x ) ^{2}} \frac{df}{d x}

Simplify

- \frac{1}{f ( x ) ^{2}} \frac{df}{d x} : - \frac{\frac{df}{d x}}{f ( x ) ^{2}}

= - \frac{\frac{df}{d x}}{f ( x ) ^{2}}

x^{\frac{1}{3}} - 1

\frac{d}{d t} (\frac{1}{( t + 1 ) ^{2}})

\int 3 x y^{2} d y

\frac{\partial}{\partial x} (e^{e^{y} (1 + e^{x}) - 2})

x^{2} - 2, - (x - 1)^{2} + 3

What is the derivative of y= 1/(f(x)) ?
The derivative of y= 1/(f(x)) is -(\frac{df)/(dx)}{f(x)^2}
What is the first derivative of y= 1/(f(x)) ?
The first derivative of y= 1/(f(x)) is -(\frac{df)/(dx)}{f(x)^2}