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Popular >

derivative of 1/({f(x)})

Solution

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

Solution

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

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

Simplify

- \frac{1}{f ( 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}}

Popular Examples

integral from 1 to-1 of (x-1)(3x+2)

\int_{1}^{- 1} (x - 1) (3 x + 2) d x

integral of x\sqrt[4]{5x+7}

derivative of 2/(sin(x+cos(x)))

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

t(dy)/(dt)=t^3+25t^3y

t \frac{d y}{d t} = t^{3} + 25 t^{3} y

integral of (ysin(xy))

\int (y sin (x y)) d x

Frequently Asked Questions (FAQ)

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