What is (\partial)/(\partial y)(sqrt(y^2-9)) ?

The answer to (\partial)/(\partial y)(sqrt(y^2-9)) is y/(sqrt(y^2-9))

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(\partial)/(\partial y)(sqrt(y^2-9))

\frac{\partial}{\partial y} (y^{2} - 9)

\frac{y}{y ^{2} - 9}

Solution steps

\frac{\partial}{\partial y} (y^{2} - 9)

Apply the chain rule:

\frac{1}{2 y ^{2} - 9} \frac{\partial}{\partial y} (y^{2} - 9)

= \frac{1}{2 y ^{2} - 9} \frac{\partial}{\partial y} (y^{2} - 9)

\frac{\partial}{\partial y} (y^{2} - 9) = 2 y

= \frac{1}{2 y ^{2} - 9} \cdot 2 y

Simplify

\frac{1}{2 y ^{2} - 9} \cdot 2 y : \frac{y}{y ^{2} - 9}

= \frac{y}{y ^{2} - 9}

\frac{d y}{d x} = - \frac{4 x + 4 y}{4 x + 9 y}

x \to 2 + lim (\frac{x - 3}{x ^{2} - 4})

\frac{\partial}{\partial y} (x^{4} + 8 x y^{7})

\int \frac{ln ∣ x ∣}{x} d x

f (t) = (3 t - 1)^{4} (2 t + 1)^{- 3}

What is (\partial)/(\partial y)(sqrt(y^2-9)) ?
The answer to (\partial)/(\partial y)(sqrt(y^2-9)) is y/(sqrt(y^2-9))