Differentiate the following with respect to x(i) y = a(x - 2)(x - b)(i

1.	Differentiate the following with respect to x(i) y = a(x - 2)(x - b)(ii) y = (ax2 + b)2
Answer» (i) y = x²- (a + b)x + ab ∴ dy/dx = 2x - (a + b) + 0 = 2x - (a + b) (ii) y = (ax² + b)² = a²x⁴ + 2abx² + b² ∴ dy/dx = a²(4x³) + 2ab(2x) + 0 = 4a²x³ + 4abx

Differentiate the following with respect to x(i) y = a(x - 2)(x - b)(ii) y = (ax2 + b)2

Answer»

(i) y = x²- (a + b)x + ab

∴ dy/dx = 2x - (a + b) + 0

= 2x - (a + b)

(ii) y = (ax² + b)²

= a²x⁴ + 2abx² + b²

∴ dy/dx = a²(4x³) + 2ab(2x) + 0

= 4a²x³ + 4abx

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