222k views
0 votes
Given y=f(x)=4ˣ²+x-1, (a)find the general formula for dy.

User Hahahaha
by
7.7k points

1 Answer

5 votes

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.

User Mina Luke
by
7.0k points