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

The derivative of 1/((x-1^2+1)) is -(2x-2)/((x^2-2x+2)^2)

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x^{2} \frac{d}{d x} (\frac{d y}{d x}) + 19 x \frac{d y}{d x} + 145 y = 0

5 y^{^{''}} + 11 y^{^{'}} + 7 y = 0, y (0) = 8, y^{^{'}} (0) = 10

\int_{0}^{1} 4 x^{3} 3 x^{4} + 4 d x

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

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

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