What is a function that could have − 8 e^ − 8 x as its derivative?

Question

What is a function that could have ^−8x as its derivative?

Answer 1

This is known as integration, a fundamental in calculus.

Take f(x) = e^3x as an example. This functions derivative is f'(x) = 3e^3x. The integral of 3e^3x + C, where C is any constant, will give you the original function, e^3x.

This is the same situation in your equation.

The function f(x) = e^-8x + 5 (or any other constant) will result in a derivative of -8e^-8x.

Try finding the derivative of e^-8x + 5 and work it out backwards after.

Answer 2

If you are working on integration, that is how you would find the answer to your questions.

Integrate -8 ∫e^-8x dx = -8 [ e^-8x/(-8) ] + C = e^-8x + C