Use the chain rule to find the derivative of the following function.𝑓(𝑟)=𝑒6𝑟2+3𝑟+5

Sure, let's find the derivative of the function f(r) = e^(6r^2 + 3r + 5) using the chain rule.

The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 1: Identify the outer and inner functions. In this case, the outer function is e^x and the inner function is 6r^2 + 3r + 5.

Step 2: Find the derivative of the outer function. The derivative of e^x is e^x.

Step 3: Find the derivative of the inner function. The derivative of 6r^2 + 3r + 5 is 12r + 3.

Step 4: Apply the chain rule. According to the chain rule, the derivative of f(r) is the derivative of the outer function times the derivative of the inner function. So, the derivative of f(r) is e^(6r^2 + 3r + 5) * (12r + 3).

So, the derivative of the function f(r) = e^(6r^2 + 3r + 5) is f'(r) = (12r + 3)e^(6r^2 + 3r + 5).