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

The answer to (\partial)/(\partial x)((x-1)(a+1+(x-1)^2)) is 3x^2-6x+a+4

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

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

3 x^{2} - 6 x + a + 4

Solution steps

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

Simplify

(x - 1) (a + 1 + (x - 1)^{2}) : (x - 1) (x^{2} - 2 x + a + 2)

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x - 1, g = x^{2} - 2 x + a + 2

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

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

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

= 1 \cdot (x^{2} - 2 x + a + 2) + (2 x - 2) (x - 1)

Simplify

1 \cdot (x^{2} - 2 x + a + 2) + (2 x - 2) (x - 1) : 3 x^{2} - 6 x + a + 4

= 3 x^{2} - 6 x + a + 4

2 (x^{2} + y^{2})^{2} = 25 (x^{2} - y^{2})

n = 1 \sum \infty \frac{( n + 1 )}{n}

\int \frac{1}{x ^{2}} - x d x

sin (3 x^{2} + cos (x))

y = 3 + cot (x) - 2 csc (x)

What is (\partial)/(\partial x)((x-1)(a+1+(x-1)^2)) ?
The answer to (\partial)/(\partial x)((x-1)(a+1+(x-1)^2)) is 3x^2-6x+a+4