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Find the rate of change of the area of an equilateral triangle of side $x$ with respect to its: (a) side; (b) perimeter. (Hint: $A=\frac{x^{2}}{4} \sqrt{3}$ )

(a) $\frac{x}{2} \sqrt{3}$(b) $\frac{x}{6} \sqrt{3}$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 7

Marginal Functions and Rates of Change

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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a. Find the rate of change…

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An equilateral triangle of…

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(a) Write the area A of an…

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The sides of an equilatera…

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Area The length $s$ of eac…

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1.The sides of an equilate…

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Find the rate of change of…

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If $A, x$, and $h$ denote …

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An isosceles triangle has …

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Rate of Change The sides o…

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The area of an equilateral…

So lentils length of side of equilateral triangle of equal literal triangle equal X. And area Equal Root three x 4 X. Is scared so we have to find a dash X. Dash X equal limerick. He tends to X 80 minus A X. Upon the minus X equal limit, He turns to X Root three x 4. The scale minus root three by four Xs. Get up on t minus X equal equal limit. He tends to X. Route three way four into T plus X. Now put equal X. So this gives Route three x 2 x four X greater than zero. Now for second part the question is saying value of X. If it is X equals A X. That is Route three x 2 x equal Route three x 4. X. is scared. That means X is care equal X is good equal two X. That means X equal to, so for X equal to a dash X equals a X. So four X equals two N. S. X equals A X.

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