What is (\partial)/(\partial y)((x^2-1)(y+2)) ?

The answer to (\partial)/(\partial y)((x^2-1)(y+2)) is x^2-1

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(\partial)/(\partial y)((x^2-1)(y+2))

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

x^{2} - 1

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (y) = 1

\frac{\partial}{\partial y} (2) = 0

= (x^{2} - 1) (1 + 0)

Simplify

= x^{2} - 1

f (x) = \frac{3}{x ^{2}}, at x = 1

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

\int e^{5 x + e^{5 x}} d x

What is (\partial)/(\partial y)((x^2-1)(y+2)) ?
The answer to (\partial)/(\partial y)((x^2-1)(y+2)) is x^2-1