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Use the appropriate rules to determine the derivative.$$f(x)=(x-2)(x+2), \text { find } f^{\prime}(x)$$

$$2 x$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 2

Derivatives Rules 1

Derivatives

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Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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00:58

Alright, This problem. You should want to dio a step before actually trying to figure out what the derivative is on. Def. You're confused. That's what this notation is that saying, Hey, find the derivative so I would do the middle step of actually distributing all this out. So we're looking at the original function is X squared plus two X and then distributing here minus two X minus four. Well, that's kind of nice. These pieces of cancel on now, when you take the derivative, you could just bring this to in front. So it's now two x two the first power. There's no need to write that to the first power. Um, see, there's nothing in between here, and we've talked already that the derivative of a constant zero, uh, just kind of takes over. Explain. Uh, it works if you put X to the zero power, which is equal to one and then zero times four will give you zero. If you add zero in there, it's not gonna change the value of the problem. Aan den again. Zero times, anything is still zero. So, um, that mostly explains that. But anyway, the correct answer is two X and we're done with this problem. Just one little step in there and then the problems really easy.

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