Final answer:
To find the general formula for dy, you need to take the derivative of the function y = f(x). Applying the power rule and sum rule, the derivative of y = 4ˣ² + x - 1 is dy = 2 * 4ˣ + 1.
Step-by-step explanation:
The general formula for dy can be found by taking the derivative of the function y = f(x). To find the derivative, you need to apply the power rule and the sum rule. The power rule states that if you have a function of the form f(x) = x^n, the derivative is f'(x) = nx^(n-1). The sum rule states that if you have a function of the form f(x) = g(x) + h(x), the derivative is f'(x) = g'(x) + h'(x).
First, let's apply the power rule to find the derivative of 4ˣ². The derivative of 4ˣ² with respect to x is 2 * 4ˣ. So, the derivative of 4ˣ² is 2 * 4ˣ.
Next, let's find the derivative of x. The derivative of x with respect to x is 1. So, the derivative of x is 1.
Finally, applying the sum rule, the derivative of y = 4ˣ² + x - 1 is dy = 2 * 4ˣ + 1.