What is the d/(dy)(sqrt(10y-y^2)) ?

The d/(dy)(sqrt(10y-y^2)) is (5-y)/(sqrt(10y-y^2))

What is the first d/(dy)(sqrt(10y-y^2)) ?

The first d/(dy)(sqrt(10y-y^2)) is (5-y)/(sqrt(10y-y^2))

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\frac{d}{d y} (10 y - y^{2})

\frac{5 - y}{10 y - y ^{2}}

Solution steps

\frac{d}{d y} (10 y - y^{2})

Apply the chain rule:

\frac{1}{2 10 y - y ^{2}} \frac{d}{d y} (10 y - y^{2})

= \frac{1}{2 10 y - y ^{2}} \frac{d}{d y} (10 y - y^{2})

\frac{d}{d y} (10 y - y^{2}) = 10 - 2 y

= \frac{1}{2 10 y - y ^{2}} (10 - 2 y)

Simplify

\frac{1}{2 10 y - y ^{2}} (10 - 2 y) : \frac{5 - y}{10 y - y ^{2}}

= \frac{5 - y}{10 y - y ^{2}}

What is the d/(dy)(sqrt(10y-y^2)) ?
The d/(dy)(sqrt(10y-y^2)) is (5-y)/(sqrt(10y-y^2))
What is the first d/(dy)(sqrt(10y-y^2)) ?
The first d/(dy)(sqrt(10y-y^2)) is (5-y)/(sqrt(10y-y^2))