Related rates, area of an equilateral triangle (calculus 1, ap calculus)

Related rates, area of an equilateral triangle, calculus 1 tutorial, ap calculus
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[@chitlitlah]

I love calculus. I took many semesters of it in college and this problem is pretty easy, but I still find myself in awe that nearly every mathematical function has a fairly simple derivative, many have a fairly simple integral, and it can so easily be used to solve problems that would seem impossible without complex computer simulations.

[@jnaderaidz9884]

Thank you brother,you're the best.

[@BenDover69831]

"1/2 is 1/2"- BPRP 2022

[@wristdisabledwriter2893]

Does this mean the area of a equilateral triangle is always sqrt(3)/4 times it’s side squared

[@rengarajramgovind5910]

Area= 1/2* 1/2x*sqrt3x/4

[@sykenomic9893]

can someone tell me why when writing da/dt he threw in the dx/dt at the end of the line?

[@supbro6505]

Chain rule. Since x is a function of t, you multiply by the derivative of x with respect to t, which is dx/dt.