Use the chain rule to find the derivative of the following function.𝑓(𝑟)=𝑒3𝑟2+9𝑟−4𝑓′(𝑟)=

Sure, let's use the chain rule to find the derivative of the function f(r) = e^(3r^2 + 9r - 4).

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.

Here, our outer function is e^x and our inner function is 3r^2 + 9r - 4.

Step 1: Find the derivative of the outer function. The derivative of e^x is e^x.

Step 2: Find the derivative of the inner function. The derivative of 3r^2 + 9r - 4 is 6r + 9.

Step 3: Apply the chain rule. According to the chain rule, the derivative of the composite function is the derivative of the outer function times the derivative of the inner function.

So, f'(r) = e^(3r^2 + 9r - 4) * (6r + 9).

That's the derivative of the function.