can someone explain to me the steps to solve this problem?
find the derivative: (3x^2+7)(x^2-2x+3)
I won't solve it but...
Since it's multiplied.
It's the multiplication rule for derivatives.
(derivative of the first equation)(second equation)+ (first equation)(derivative of the second equation)
3x^4-6x^3+16x^2-14x+21
Of course! To find the derivative of the expression (3x^2 + 7)(x^2 - 2x + 3), we can use the product rule of differentiation. The product rule states that the derivative of the product of two functions is equal to the derivative of the first function, times the second function, plus the first function times the derivative of the second function.
Step 1: Identify the two functions being multiplied together.
In this case, the two functions being multiplied are (3x^2 + 7) and (x^2 - 2x + 3).
Step 2: Find the derivative of each individual function.
The derivative of (3x^2 + 7) is 6x, since the derivative of x^n (where n is a constant) is nx^(n-1). The derivative of (x^2 - 2x + 3) is 2x - 2, using the same rule.
Step 3: Apply the product rule.
Using the product rule, we can now calculate the derivative of the expression. The derivative of the product (3x^2 + 7)(x^2 - 2x + 3) is equal to:
(3x^2 + 7)(2x - 2) + (x^2 - 2x + 3)(6x).
Step 4: Simplify the expression obtained in Step 3.
To simplify the expression, distribute the terms and combine like terms if necessary. This will give you the final result.
So, the steps to solve the problem and find the derivative of (3x^2 + 7)(x^2 - 2x + 3) are as follows:
1. Identify the functions being multiplied: (3x^2 + 7) and (x^2 - 2x + 3).
2. Find the derivative of each function: (3x^2 + 7) becomes 6x, and (x^2 - 2x + 3) becomes 2x - 2.
3. Apply the product rule: (3x^2 + 7)(2x - 2) + (x^2 - 2x + 3)(6x).
4. Simplify the expression to obtain the final result.