What is the d/(dy)(1/(1+y^2)) ?

The d/(dy)(1/(1+y^2)) is -(2y)/((1+y^2)^2)

What is the first d/(dy)(1/(1+y^2)) ?

The first d/(dy)(1/(1+y^2)) is -(2y)/((1+y^2)^2)

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the d/(dy)(1/(1+y^2)) ?
The d/(dy)(1/(1+y^2)) is -(2y)/((1+y^2)^2)
What is the first d/(dy)(1/(1+y^2)) ?
The first d/(dy)(1/(1+y^2)) is -(2y)/((1+y^2)^2)