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Differentiate the function.$ G(q) = (1 + q^{-1})^2 $

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$$G^{\prime}(q)=0+2\left(-1 q^{-2}\right)+\left(-2 q^{-3}\right)=-2 q^{-2}-2 q^{-3}$$

00:38

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Missouri State University

Campbell 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.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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he had squares, the one you made here. So we have the square of a sum, which is G of Q is equal to cute the negative, too, plus too cute to the negative one plus one. And we're going to use to some indifference rule. So G, the derivative of G of Q is equal to de over de que cute, the negative, too, plus de over D. Q. Too cute to the negative one plus de over D. Q. For one, we used the constant function role. Just become zero. And when we use the constant multiple rule and the power roll, we could take thes outside and it becomes negative to Q to the negative to minus one plus two times negative one Cute, the negative one minus one. This equals negative. Too cute The negative three times one plus que.

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