What is the derivative of (x-1^2*(x-2)*(x-4)) ?

The derivative of (x-1^2*(x-2)*(x-4)) is 4x^3-24x^2+42x-22

What is the first derivative of (x-1^2*(x-2)*(x-4)) ?

The first derivative of (x-1^2*(x-2)*(x-4)) is 4x^3-24x^2+42x-22

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\frac{d}{d x} ((x - 1)^{2} \cdot (x - 2) \cdot (x - 4))

4 x^{3} - 24 x^{2} + 42 x - 22

Solution steps

\frac{d}{d x} ((x - 1)^{2} (x - 2) (x - 4))

Apply the Product Rule:

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

f = (x - 1)^{2}, g = (x - 2) (x - 4)

= \frac{d}{d x} ((x - 1)^{2}) (x - 2) (x - 4) + \frac{d}{d x} ((x - 2) (x - 4)) (x - 1)^{2}

\frac{d}{d x} ((x - 1)^{2}) = 2 (x - 1)

\frac{d}{d x} ((x - 2) (x - 4)) = 2 x - 6

= 2 (x - 1) (x - 2) (x - 4) + (2 x - 6) (x - 1)^{2}

Simplify

2 (x - 1) (x - 2) (x - 4) + (2 x - 6) (x - 1)^{2} : 4 x^{3} - 24 x^{2} + 42 x - 22

= 4 x^{3} - 24 x^{2} + 42 x - 22

x^{7} - 3 x^{4} + 7 x^{3} + 43, at x = - 2

\int \frac{1}{x 1 + x} d x

x \to 0 lim (3 - 4 x)

\int x^{2} + 81 d x

x \to 0 lim (3 x)

What is the derivative of (x-1^2*(x-2)*(x-4)) ?
The derivative of (x-1^2*(x-2)*(x-4)) is 4x^3-24x^2+42x-22
What is the first derivative of (x-1^2*(x-2)*(x-4)) ?
The first derivative of (x-1^2*(x-2)*(x-4)) is 4x^3-24x^2+42x-22