Question

Derivitave of (2x-3)(x^2-2) ​

Answer 1

The derivative of (2x-3)(x²-2) is found using the product rule, resulting in 6x² - 6x - 4.

Step-by-step explanation:

The derivative of the function (2x-3)(x²-2) can be found using the product rule. The product rule states that if you have two functions f(x) and g(x), the derivative of their product f(x)g(x) is f'(x)g(x) + f(x)g'(x).

Let f(x) = (2x-3) and g(x) = (x²-2). Then, find the derivatives of f(x) and g(x) separately:

• f'(x) = derivative of (2x - 3) = 2
• g'(x) = derivative of (x² - 2) = 2x

Now apply the product rule:

derivative of (2x-3)(x²-2) = f'(x)g(x) + f(x)g'(x)
= 2(x²-2) + (2x-3)(2x)
= 2x² - 4 + 4x² - 6x
= 6x² - 6x - 4

Answer 2

d/dx [f(x)g(x)]=
f(x)d/dx[g(x)]+g(x)d/dx[f(x)]
6x^2-6x-4