What is the d/(dy)(sqrt(4-y^2)) ?

The d/(dy)(sqrt(4-y^2)) is -y/(sqrt(4-y^2))

What is the first d/(dy)(sqrt(4-y^2)) ?

The first d/(dy)(sqrt(4-y^2)) is -y/(sqrt(4-y^2))

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\frac{d}{d y} (4 - y^{2})

- \frac{y}{4 - y ^{2}}

Solution steps

\frac{d}{d y} (4 - y^{2})

Apply the chain rule:

\frac{1}{2 4 - y ^{2}} \frac{d}{d y} (4 - y^{2})

= \frac{1}{2 4 - y ^{2}} \frac{d}{d y} (4 - y^{2})

\frac{d}{d y} (4 - y^{2}) = - 2 y

= \frac{1}{2 4 - y ^{2}} (- 2 y)

Simplify

\frac{1}{2 4 - y ^{2}} (- 2 y) : - \frac{y}{4 - y ^{2}}

= - \frac{y}{4 - y ^{2}}

\int_{- 7}^{0} (4 + 49 - x^{2}) d x

\int \frac{2 x ^{2} + 5 x + 2}{( x ^{2} + 1 ) ^{2}} d x

e^{y^{2}} d x + x^{2} y d y = 0

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = e^{x}

\int \frac{25 - 16 x ^{2}}{x} d x

What is the d/(dy)(sqrt(4-y^2)) ?
The d/(dy)(sqrt(4-y^2)) is -y/(sqrt(4-y^2))
What is the first d/(dy)(sqrt(4-y^2)) ?
The first d/(dy)(sqrt(4-y^2)) is -y/(sqrt(4-y^2))