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Popular >

derivative of 1/((x^2-1))

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

-45y^{''}+35y^'=0,y(2)=2,y^'(-1)=-1

- 45 y^{^{''}} + 35 y^{^{'}} = 0, y (2) = 2, y^{^{'}} (- 1) = - 1

(x + e^{y}) d y - d x = 0

integral of (3(2^x)-2(3^x))/(2^x)

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

derivative of x+9

\frac{d}{d x} (x + 9)

limit as x approaches 5 of 3x^2-x-2

x \to 5 lim (3 x^{2} - x - 2)

Frequently Asked Questions (FAQ)

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