What is the derivative of sqrt(81-y^2) ?

The derivative of sqrt(81-y^2) is -y/(sqrt(81-y^2))

What is the first derivative of sqrt(81-y^2) ?

The first derivative of sqrt(81-y^2) is -y/(sqrt(81-y^2))

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derivative of

81 - y^{2}

- \frac{y}{81 - y ^{2}}

Solution steps

\frac{d}{d y} (81 - y^{2})

Apply the chain rule:

\frac{1}{2 81 - y ^{2}} \frac{d}{d y} (81 - y^{2})

= \frac{1}{2 81 - y ^{2}} \frac{d}{d y} (81 - y^{2})

\frac{d}{d y} (81 - y^{2}) = - 2 y

= \frac{1}{2 81 - y ^{2}} (- 2 y)

Simplify

\frac{1}{2 81 - y ^{2}} (- 2 y) : - \frac{y}{81 - y ^{2}}

= - \frac{y}{81 - y ^{2}}

What is the derivative of sqrt(81-y^2) ?
The derivative of sqrt(81-y^2) is -y/(sqrt(81-y^2))
What is the first derivative of sqrt(81-y^2) ?
The first derivative of sqrt(81-y^2) is -y/(sqrt(81-y^2))