Find the derivatives of the following: 1. y = (x-d) (x-b) 2. y = (ax^2 + b)^2 3. y = (x-a)/(x-b)

Question

Find the derivatives of the following:

1. y = (x - d)(x - b)

2. y = (ax² + b²)

3. y = \(\frac{x-a}{x-b}\)

4. y = x^-3 (5 + 3x)

Answer 1

1. \(\frac{dy}{dx}\) = (x- a)\(\frac{d}{dx} (x-b)\) + (x - b)\(\frac{d}{dx} (x-a)\)

= (x – a) × 1 + (x – b) × 1 

= x – a + x – b = 2x – a – b

2. y = a² x⁴ + b² + 2abx²

^{\(\frac{dy}{dx}\) =} 4a² x³ + 4abx

3.

4. y = 5x^-3 + 3x^-2

\(\frac{dy}{dx}\) = 5(-3)x^-3-1 + 3(-2)x^2-1

= -15 x^-4 - 6x^-3