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

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

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

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

2 x (y + 2)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (1) = 0

= (y + 2) (2 x - 0)

Simplify

= 2 x (y + 2)

\int_{- 2}^{1} x^{2} + x - 2 d x

\int (2 x (x^{2} + 2)^{2}) d x

t sin (t) + cos (t)

2 t^{2} \frac{d x}{d t} = 3 t x + x^{2}

y = \frac{5}{4 x ^{3}}

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