Question

Find the derivative of the following 3

(i) 2x - 3/4

(ii) (5x³ + 3x - 1)(x - 1)

(iii) x⁵(3 - 6x^-9)

(iv) x^-4(3 - 4x^-5)

(v) 2/(x + 1) - x²/(3x - 1)

Answer 1

(i) 2x - 3/4

Let y  = f(x) = 2x - 3/4

Then, derivative of given function

Hence, derivative of given function (2x - 3/4)

(ii) (5x³ + 3x - 1)(x - 1)

Let y = f(x) = (5x³ + 3x – 1) (x – 1)

The given function is product of two function.

Then, derivative of product of two functions

= 20x³ – 15x² + 6x – 4

Hence, derivative of given function 

= 20x³ – 15x² + 6x – 4.

(iii) x⁵(3 - 6x^-9)

Let y = x⁵(3 – 6x^-9)

Then, derivative of given function

= 15x⁴ + 24/x⁵

(iv) x^-4(3 - 4x^-5)

(v) 2/(x + 1) - x²/(3x - 1)

[From the formula of derivative of quotient of two functions]

We can also solve this equation by product rule of derivative.