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

The derivative of (2-x(1-2x)) is 4x-5

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

The first derivative of (2-x(1-2x)) is 4x-5

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

4 x - 5

Solution steps

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

Apply the Product Rule:

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

f = 2 - x, g = 1 - 2 x

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

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

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

= (- 1) (1 - 2 x) + (- 2) (2 - x)

Simplify

(- 1) (1 - 2 x) + (- 2) (2 - x) : 4 x - 5

= 4 x - 5

What is the derivative of (2-x(1-2x)) ?
The derivative of (2-x(1-2x)) is 4x-5
What is the first derivative of (2-x(1-2x)) ?
The first derivative of (2-x(1-2x)) is 4x-5