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junior college 2 | H2 Maths
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Date Posted: 3 years ago
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Alternative method : Perform implicit differentiation
eʸ = x³ + 2 ln x
Differentiate both sides with respect to x,
eʸ dy/dx = 3x² + 2/x
dy/dx = (2x² + 2/x) / eʸ
dy/dx = (2x² + 2/x) / (x³ + 2 ln x)
When x = 1, dy/dx = (2(1²) + 2/1) / (1³ + 2 ln1)
= 5 / 1
= 5
eʸ = x³ + 2 ln x
Differentiate both sides with respect to x,
eʸ dy/dx = 3x² + 2/x
dy/dx = (2x² + 2/x) / eʸ
dy/dx = (2x² + 2/x) / (x³ + 2 ln x)
When x = 1, dy/dx = (2(1²) + 2/1) / (1³ + 2 ln1)
= 5 / 1
= 5
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