Differentiate the following equation using product rule. Simplify the answers.
y = x³ +2 3x²-x
Since the way you typed would not require a product rule, I will assume you meant:
y = (x^3+2)(3x^2-2)
dy/dx = (x^3 + 2)(6x) + (3x^2 - 2)(3x^2)
expand and simplify if you feel like it
If you meant something different .....
the product of the zeroes of the polynomial 3x² + 5x -4k is -8, then the value of k is:
1 point
15
-10
10
6
To differentiate the equation y = x³ + 2 * 3x² - x using the product rule, we need to differentiate each term separately and then combine them.
First, let's identify the two terms involved in the product rule:
Term1: x³
Term2: 2 * 3x² - x
Now, let's differentiate each term:
For Term1 (x³):
The derivative of x³ with respect to x can be found using the power rule. The power rule states that d/dx (x^n) = nx^(n-1).
So, differentiating x³, we get 3x².
For Term2 (2 * 3x² - x):
We have two sub-terms in Term2, namely 2 * 3x² and -x.
To differentiate each sub-term, we can treat them as separate terms.
For the sub-term 2 * 3x²:
Differentiating 2 * 3x², we get:
- The derivative of the constant term 2 is 0.
- The derivative of 3x² can be found using the power rule. Differentiating 3x², we get 6x.
For the sub-term - x:
The derivative of -x is simply -1.
Now, let's combine the derivatives:
The derivative of y = x³ + 2 * 3x² - x would be:
dy/dx = (3x²) + (2 * 6x) + (-1)
Simplifying the answer, we get:
dy/dx = 3x² + 12x - 1
Therefore, the simplified answer is dy/dx = 3x² + 12x - 1.