PLEASE HELP Find the first and second derivatives of the function.
y = e^8ex. I keep getting y' = e^8ex * 8 and its wrong. how do you do this?
y=e^(8e^x)
use the chain rule,
dy/dx
= dy/d(8e^x) . d(8e^x)/dx
= e^(8e^x) . 8e^x
=8 e^(8e^x).e^x
=8 e^(8e^x+x)
To find the first and second derivatives of the function y = e^8ex, you can use the chain rule.
Let's start with finding the first derivative (dy/dx):
Step 1: Identify the function within the function. In this case, the inner function is 8ex.
Step 2: Find the derivative of the inner function with respect to x. The derivative of ex is ex.
Step 3: Multiply the derivative of the inner function by the derivative of the outer function. The derivative of e^u, where u is a function of x, is simply e^u times the derivative of u with respect to x. Therefore, we have e^8ex * ex.
So, the first derivative of y = e^8ex is dy/dx = e^8ex * ex.
Now, let's move on to finding the second derivative (d^2y/dx^2):
To find the second derivative, we need to take the derivative of the first derivative.
Step 1: Use the product rule to differentiate e^8ex * ex.
- The derivative of e^8ex is e^8ex * 8ex.
- The derivative of ex is ex.
Step 2: Multiply the derivative of the first term (e^8ex * 8ex) by the second term (ex).
So, the second derivative of y = e^8ex is d^2y/dx^2 = (e^8ex * 8ex) * ex, which simplifies to d^2y/dx^2 = 8e^9ex^2.