How do you differentiate #f(x)=(x^4-1)(e^x-2)# using the product rule?
You must apply the chain rule alongside some derivative results
The chain rule reads, for two given functions
IMP . in case your functions are not a function of the independent variables directly, e.g. you make the derivative regarding the time, not x, you must pay attention to that, some previous maneuver must be done.
Now you must solve the derivatives one by one:
Use the linearity property of derivative, the derivative of the sum is the sum of the derivatives, it is a linear operator. Then remember that the derivative of polynomial is just the subtraction of the exponent, multiplied by the previous exponent.
Finally, remember that the derivative of a constant is zero.
For the exponential, just remember that the derivative of the exponential is itself.
Finally you get:
If you want you can simply the expression, but for now it is not needed.