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Use your knowledge of the derivative to compute the limit given.$$\lim _{h \rightarrow 0} \frac{\frac{1}{(x+h)^{2}}-\frac{1}{x^{2}}}{h}$$

$$\frac{-2}{x^{3}}$$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 2

Derivatives Rules 1

Derivatives

Harvey Mudd College

Baylor University

Boston College

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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What we're looking at in this problem is the limit definition of the derivative. And the limit definition is a Z H approaches zero of F FX plus age minus F of X all over H s. Oh, this is equal to F prime of X as long as you identify what f of X is equal to. And since I mentioned it's ffx plus H minus ffx, it's pretty straightforward that you recognize that f of X is equal to that one over x squared piece. Um, yeah, And from here I would just rewrite that as X to the native second power. That's a rule with exponents. So when they ask you to evaluate its basically saying what's the derivative of that piece? What I have in blue, will you bring that negative two in front and you subtract one from that exponents and some teachers will let you leave your answer like this, or you might have a teacher that wants you to rewrite it. Uh, negative two is still there, and with a negative exponents to get back into the denominator just like that, I guess I should write or here instead

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