Eric Nicholas K's answer to LockB's Secondary 4 A Maths Singapore question.
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The validity is simply due to that square root stuff.
For the second part, we just sub in and inspect the elements accordingly. You will only learn a different method of obtaining the equation in part ii by a method called implicit differentiation, taught in the A Levels if you are pursuing studies in the A Levels.
For the second part, we just sub in and inspect the elements accordingly. You will only learn a different method of obtaining the equation in part ii by a method called implicit differentiation, taught in the A Levels if you are pursuing studies in the A Levels.
Date Posted:
3 years ago
Alternative to ii) :
y = x²√(9 - 2x²)
y = √(x⁴(9 - 2x²))
y = √(9x⁴ - 2x⁶) = (9x⁴ - 2x⁶)¹/²
dy/dx = ½ (9x⁴ - 2x⁶)-¹/² (36x³ - 12x⁵)
dy/dx = (18x³ - 6x⁵) / √(9x⁴ - 2x⁶)
Multiply by √(9x⁴ - 2x⁶) on both sides,
√(9x⁴ - 2x⁶) dy/dx = 18x³ - 6x⁵
y dy/dx = 18x³ - 6x⁵
[Since y = √(9x⁴ - 2x⁶), rewrite the one on the LHS as y]
y dy/dx + 6x⁵ - 18x³ = 0
y dy/dx + 6x³(x² - 3) = 0
(Shown)
y = x²√(9 - 2x²)
y = √(x⁴(9 - 2x²))
y = √(9x⁴ - 2x⁶) = (9x⁴ - 2x⁶)¹/²
dy/dx = ½ (9x⁴ - 2x⁶)-¹/² (36x³ - 12x⁵)
dy/dx = (18x³ - 6x⁵) / √(9x⁴ - 2x⁶)
Multiply by √(9x⁴ - 2x⁶) on both sides,
√(9x⁴ - 2x⁶) dy/dx = 18x³ - 6x⁵
y dy/dx = 18x³ - 6x⁵
[Since y = √(9x⁴ - 2x⁶), rewrite the one on the LHS as y]
y dy/dx + 6x⁵ - 18x³ = 0
y dy/dx + 6x³(x² - 3) = 0
(Shown)
LockB :
The goal of this question is is for students to realise that multiplying by y on LHS is the same as multiplying by the square root term on the RHS, eventually reaching the desired equation by bringing terms over to the other side.
Inspection is merely verifying and only leads to the conclusion that 'oh, so its correct and it fits' but misses out the above skill of realising that there needs to be a multiplication by y from dy/dx to get y dy/dx.
The goal of this question is is for students to realise that multiplying by y on LHS is the same as multiplying by the square root term on the RHS, eventually reaching the desired equation by bringing terms over to the other side.
Inspection is merely verifying and only leads to the conclusion that 'oh, so its correct and it fits' but misses out the above skill of realising that there needs to be a multiplication by y from dy/dx to get y dy/dx.
thx :)
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