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This level of difficulty will not be seen in an O-level paper...
Date Posted:
3 years ago
okay thank you
The answer should be :
6 (6 cos⁷(3x + x²) - 4x²)⁵ [-42 (3 + 2x) sin(3x + x²) cos⁶(3x + x²) - 8x]
= -12 (6 cos⁷(3x + x²) - 4x²)⁵ [21(3 + 2x) sin(3x + x²) cos⁶(3x + x²) + 4x]
= -12 (2(3 cos⁷(3x + x²) - 2x²))⁵ [21(3 + 2x) sin(3x + x²) cos⁶(3x + x²) + 4x]
= -12(2⁵) (3 cos⁷(3x + x²) - 2x²)⁵ [21(3 + 2x) sin(3x + x²) cos⁶(3x + x²) + 4x]
= -384 (3 cos⁷(3x + x²) - 2x²)⁵ [21(3 + 2x) sin(3x + x²) cos⁶(3x + x²) + 4x]
6 (6 cos⁷(3x + x²) - 4x²)⁵ [-42 (3 + 2x) sin(3x + x²) cos⁶(3x + x²) - 8x]
= -12 (6 cos⁷(3x + x²) - 4x²)⁵ [21(3 + 2x) sin(3x + x²) cos⁶(3x + x²) + 4x]
= -12 (2(3 cos⁷(3x + x²) - 2x²))⁵ [21(3 + 2x) sin(3x + x²) cos⁶(3x + x²) + 4x]
= -12(2⁵) (3 cos⁷(3x + x²) - 2x²)⁵ [21(3 + 2x) sin(3x + x²) cos⁶(3x + x²) + 4x]
= -384 (3 cos⁷(3x + x²) - 2x²)⁵ [21(3 + 2x) sin(3x + x²) cos⁶(3x + x²) + 4x]
J's answer is correct. Made 2 major errors in my working...
I suspect this question is only provided to the student to be familiar with the correct timings to apply the chain rule. Otherwise, the question seems to have little practical value.
This question is a good test of whether the student knows the chain rule well or not.