EACH SIDE OF A SQUARE IS INCREASING AT A RATE OF 6 CM/S. AT WHAT RATE IS THE AREA OF THE SQUARE...

Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square increasing when the area of the square is 16cm^2?
This related rates square problem is a good example of a related rates calculus word problem. Even if you don't have this specific problem required for homework, this related rates area of a square problem is a good demonstration of techniques that can be used in other related rates problems dealing with related rates and other geometric shapes. That's because it can be solved using the same 4 step process as all other related rates calculus word problems:
0:00 Each side of a square is increasing at a rate of 6 cm/s
0:30 Draw a sketch
2:05 Come up with your equation
4:13 Implicit Differentiation
5:59 Solve For the Desired Rate of Change
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[@JakesMathLessons]

0:00 Each side of a square is increasing at a rate of 6 cm/s
0:30 Draw a sketch
2:05 Come up with your equation
4:13 Implicit Differentiation
5:59 Solve For the Desired Rate of Change

[@safwansadiq3029]

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[@JakesMathLessons]

XForceGaming thank you! So glad you like my videos!

[@alizakhan1284]

Super helpful! Was stuck on this for a while.

[@JakesMathLessons]

I’m glad you found it helpful!

[@Allahu_Akbar_the_one]

Quick question: 5:06 you've said to use "chain rule" but then you've done the power rule which was simply 2l
Were you trying to explain where they dl/dt was coming from?

[@JakesMathLessons]

Yes exactly! Since you’re taking the derivative with respect to t, you have to treat l as a function of t, so think of it as [l(t)]^2 with l(t) being the inside function and the ^2 part being the outside function. Then apply chain rule from there. We use power rule to find the derivative of the ^2 part, but the dl/dt comes from applying chain rule.

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[@JakesMathLessons]

You’re welcome!

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[@JakesMathLessons]

Thank you!

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[@JakesMathLessons]

I’m glad! You’re welcome!

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Thank you so much!

[@JakesMathLessons]

You’re welcome!

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[@JakesMathLessons]

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[@JakesMathLessons]

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[@JakesMathLessons]

You’re welcome, happy to help!