What is the derivative of 1/({f(x)(x)^{-1}(x)}) ?

The derivative of 1/({f(x)(x)^{-1}(x)}) is -(derivative of {f}(x))/({f)(x)^2}

What is the first derivative of 1/({f(x)(x)^{-1}(x)}) ?

The first derivative of 1/({f(x)(x)^{-1}(x)}) is -(derivative of {f}(x))/({f)(x)^2}

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

d s = 2 s d t

n = 0 \sum \infty 5 (- \frac{1}{3})^{n}

x \to 4 lim (\frac{( x ^{2} - 16 )}{2 - x})

\frac{d}{d x} (ln (2 e^{- x} sin (x)))

\int 1 + (tan (x))^{2} d x

What is the derivative of 1/({f(x)(x)^{-1}(x)}) ?
The derivative of 1/({f(x)(x)^{-1}(x)}) is -(derivative of {f}(x))/({f)(x)^2}
What is the first derivative of 1/({f(x)(x)^{-1}(x)}) ?
The first derivative of 1/({f(x)(x)^{-1}(x)}) is -(derivative of {f}(x))/({f)(x)^2}