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junior college 2 | H2 Maths
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Please help to show thank you!!
Date Posted: 3 years ago
Views: 478
So second part you can do right?
Only need first part?
Only need first part?
yup! Just need help to show first part :)
y = √(1 + tan-¹x)
y² = 1 + tan-¹x
Using implicit differentiation, differentiate both sides with respect to x,
2y dy/dx = 1/(1 + x²)
2y dy/dx = (1 + x²)-¹
(See MF26 for derivatives of the inverse trigo functions)
Differentiate again,
(2 dy/dx)(dy/dx) + 2y d²y/dx² = (-1)(1 + x²)-² (2x)
2y d²y/dx² + 2(dy/dx)² = -2x/(1+x²)²
y d²y/dx² + (dy/dx)² = -x/(1+x²)²
(Shown)
y² = 1 + tan-¹x
Using implicit differentiation, differentiate both sides with respect to x,
2y dy/dx = 1/(1 + x²)
2y dy/dx = (1 + x²)-¹
(See MF26 for derivatives of the inverse trigo functions)
Differentiate again,
(2 dy/dx)(dy/dx) + 2y d²y/dx² = (-1)(1 + x²)-² (2x)
2y d²y/dx² + 2(dy/dx)² = -2x/(1+x²)²
y d²y/dx² + (dy/dx)² = -x/(1+x²)²
(Shown)
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