how do you figure out the derivative, can you give an easy explanation. examples: -100 + 132Q - 20Q^2
example: A/(A + 8)
To find the derivative of a function, you can follow a few steps:
1. Identify the function and assign a variable to it. For example, in the first example, let's assign the function as f(Q) = -100 + 132Q - 20Q^2.
2. Apply the power rule: If you have a term with a variable raised to a power, bring down the power as the coefficient and decrease the power by 1. For example, for the second term (132Q), the derivative will be (132 * 1) = 132. For the third term (-20Q^2), the derivative will be (-20 * 2Q) = -40Q.
3. Differentiate any constant term, which becomes zero. In the first term (-100), the derivative will be zero.
4. Combine the derivatives of all the terms to find the derivative of the entire function. In this case, the derivative of f(Q) = -100 + 132Q - 20Q^2 will be: (0 + 132 - 40Q) = 132 - 40Q.
Let's move on to the second example:
1. Assign the function as g(A) = A/(A + 8).
2. Apply the quotient rule: The derivative of a quotient is found by taking the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator. So, g'(A) = [(A + 8) * 1 - A * 1] / (A + 8)^2.
3. Simplify the expression: g'(A) = (A + 8 - A) / (A + 8)^2 = 8 / (A + 8)^2.
That's how you can find the derivatives of these functions!