# How do you differentiate #f(x)=(x^4-1)(e^x-2)# using the product rule?

##### 1 Answer

You must apply the chain rule alongside some derivative results

#### Explanation:

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.

So:

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.