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

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

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

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

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

\frac{y}{1 + y ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 1 + y ^{2}} \cdot 2 y

Simplify

\frac{1}{2 1 + y ^{2}} \cdot 2 y : \frac{y}{1 + y ^{2}}

= \frac{y}{1 + y ^{2}}

f (x) = 2 x^{2} + 4, at x = - 2

z \to 1 + i lim (z^{2} - 5 z + 10)

y^{^{'}} = 2 y - 4 x

x \to - 3 lim (\frac{x}{x + 3})

x \to 0 lim (\frac{x - x cos ( x )}{sin ^{2} ( 3 x )})

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