# 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

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.

By signing up, you agree to our Terms of Service and Privacy Policy

To differentiate ( f(x) = (x^4 - 1)(e^x - 2) ) using the product rule:

- Apply the product rule, which states that the derivative of the product of two functions ( u(x) ) and ( v(x) ) is given by ( u'(x)v(x) + u(x)v'(x) ).
- Let ( u(x) = x^4 - 1 ) and ( v(x) = e^x - 2 ).
- Calculate the derivatives ( u'(x) ) and ( v'(x) ).
- ( u'(x) = 4x^3 ) (using the power rule)
- ( v'(x) = e^x ) (derivative of ( e^x ) is itself)

- Apply the product rule formula: ( f'(x) = u'(x)v(x) + u(x)v'(x) ) ( f'(x) = (4x^3)(e^x - 2) + (x^4 - 1)(e^x) )
- Simplify the expression if necessary.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7