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junior college 1 | H2 Maths
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Date Posted: 4 years ago
Views: 308
y = (sin-¹x)²
dy/dx = 2(sin-¹x)(1/√(1 - x²))
(dy/dx)² = 2²(sin-¹x)²/(√(1 - x²))²
(dy/dx)² = 4y/(1-x²)
(1-x²)(dy/dx)² = 4y
(Proved)
dy/dx = 2(sin-¹x)(1/√(1 - x²))
(dy/dx)² = 2²(sin-¹x)²/(√(1 - x²))²
(dy/dx)² = 4y/(1-x²)
(1-x²)(dy/dx)² = 4y
(Proved)
(1-x²)(dy/dx)² = 4y
Differentiate both sides with respect to x,
(1 - x²)(2)(dy/dx)(d²y/dx²) + (-2x)(dy/dx)² = 4dy/dx
2(1 - x²)(dy/dx)(d²y/dx²) -2x(dy/dx)² - 4dy/dx = 0
2(dy/dx) ( (1 - x²)(d²y/dx²) - x(dy/dx) - 2 ) = 0
dy/dx = 0 or (1 - x²)(d²y/dx²) - x(dy/dx) - 2 = 0
(Deduced)
Differentiate both sides with respect to x,
(1 - x²)(2)(dy/dx)(d²y/dx²) + (-2x)(dy/dx)² = 4dy/dx
2(1 - x²)(dy/dx)(d²y/dx²) -2x(dy/dx)² - 4dy/dx = 0
2(dy/dx) ( (1 - x²)(d²y/dx²) - x(dy/dx) - 2 ) = 0
dy/dx = 0 or (1 - x²)(d²y/dx²) - x(dy/dx) - 2 = 0
(Deduced)
See 1 Answer
done
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clear
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Something like this would be good. Remember to continue to use chain rule and product rule as usual.
Date Posted:
4 years ago
sin‾¹(x) = ± √y
Thank you!!!!
Oops
That's why in my working I squared straight away to do away with writing the ±√y
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