What is the d/(dy)(sqrt(a^2-y^2)) ?

The d/(dy)(sqrt(a^2-y^2)) is -y/(sqrt(a^2-y^2))

What is the first d/(dy)(sqrt(a^2-y^2)) ?

The first d/(dy)(sqrt(a^2-y^2)) is -y/(sqrt(a^2-y^2))

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\frac{d}{d y} (a^{2} - y^{2})

- \frac{y}{a ^{2} - y ^{2}}

Solution steps

\frac{d}{d y} (a^{2} - y^{2})

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{y}{a ^{2} - y ^{2}}

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What is the d/(dy)(sqrt(a^2-y^2)) ?
The d/(dy)(sqrt(a^2-y^2)) is -y/(sqrt(a^2-y^2))
What is the first d/(dy)(sqrt(a^2-y^2)) ?
The first d/(dy)(sqrt(a^2-y^2)) is -y/(sqrt(a^2-y^2))