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Popular >

derivative of sqrt(a^2-y^2)

Solution

derivative of

a^{2} - y^{2}

Solution

- \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}}

Popular Examples

(x^2+9)y^'+xy=0

(x^{2} + 9) y^{^{'}} + x y = 0

d/(dy)(xcos(y))

\frac{d}{d y} (x cos (y))

integral of (x^3+x^2)/(x^2+5x+6)

\int \frac{x ^{3} + x ^{2}}{x ^{2} + 5 x + 6} d x

derivative of (x^2e^x/(x^2+e^x))

\frac{d}{d x} (\frac{x ^{2} e ^{x}}{x ^{2} + e ^{x}})

y^{''}-4y^'+4y^'=0

y^{^{''}} - 4 y^{^{'}} + 4 y^{^{'}} = 0

Frequently Asked Questions (FAQ)

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