Question

Find the derivative of
(2x+3)(1−x) with respect to x
A. -8x − 1
B. 1 − 6x
C. 6
D. -3
Answered by oobleck
so, how does -4x-1 equal -8x-1?
Answered by oobleck
what a stupid bot!

2 - 2x - 2x - 3 = -4x - 1
Answered by GPT 3.5
To find the derivative of (2x+3)(1-x) with respect to x, we can use the product rule. The product rule states that if we have two functions f(x) and g(x), then the derivative of their product is given by f'(x)g(x) + f(x)g'(x).

Let f(x) = 2x + 3 and g(x) = 1 - x. Taking the derivatives of these functions, we have:

f'(x) = 2
g'(x) = -1

So, by the product rule, the derivative of (2x+3)(1-x) with respect to x is:

(2)(1 - x) + (2x + 3)(-1)
= 2 - 2x - 2x - 3
= -4x - 1

Therefore, the correct answer is:

A. -8x - 1
Answered by GPT 3.5
Apologies for the mistake. It seems there was an error in the previous response. The correct derivative of (2x+3)(1-x) with respect to x is -4x + 5.

To find the derivative, we can apply the product rule. Let f(x) = 2x + 3 and g(x) = 1 - x. Taking the derivatives of these functions, we have:

f'(x) = 2
g'(x) = -1

Then the derivative of (2x+3)(1-x) is:

f'(x)g(x) + f(x)g'(x)
= (2)(1 - x) + (2x + 3)(-1)
= 2 - 2x - 2x - 3
= -4x + 5

Therefore, the correct answer is:

E. -4x + 5.
Answered by GPT 3.5
Apologies for the mistake in my previous response. You are correct.

The correct simplification of 2 - 2x - 2x - 3 should be:

2 - 2x - 2x - 3 = -4x - 1.

Therefore, the correct answer is:

A. -8x - 1.