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

The d/(dy)(1/(sqrt(y^2+1))) is -y/((y^2+1)^{3/2)}

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

The first d/(dy)(1/(sqrt(y^2+1))) is -y/((y^2+1)^{3/2)}

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

- \frac{y}{( y ^{2} + 1 ) ^{\frac{3}{2}}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{2 ( y ^{2} + 1 ) ^{\frac{3}{2}}} \frac{d}{d y} (y^{2} + 1)

= - \frac{1}{2 ( y ^{2} + 1 ) ^{\frac{3}{2}}} \frac{d}{d y} (y^{2} + 1)

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

= - \frac{1}{2 ( y ^{2} + 1 ) ^{\frac{3}{2}}} \cdot 2 y

Simplify

- \frac{1}{2 ( y ^{2} + 1 ) ^{\frac{3}{2}}} \cdot 2 y : - \frac{y}{( y ^{2} + 1 ) ^{\frac{3}{2}}}

= - \frac{y}{( y ^{2} + 1 ) ^{\frac{3}{2}}}

y^{^{'}} + 2 x y = 2 x^{3}

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

\int_{0}^{4} 4 x d x

\int \frac{sin ( x )}{( 1 + cos ( x ) ) ^{3}} d x

x^{^{''}} = 0

What is the d/(dy)(1/(sqrt(y^2+1))) ?
The d/(dy)(1/(sqrt(y^2+1))) is -y/((y^2+1)^{3/2)}
What is the first d/(dy)(1/(sqrt(y^2+1))) ?
The first d/(dy)(1/(sqrt(y^2+1))) is -y/((y^2+1)^{3/2)}