Question

Using product rule,differentiate the following with respect to x:

(i) y = x⁵(3 - 6x^-9)

(ii) y = x^-4(3 - 4^-5)

Answer 1

(i) dy/dx = x⁵d/dx(3 - 6x^-9) + (3 - 6x^-9) d/dxx⁵

= x⁵(0 - 6(-9x^-10)) + (3 - 6x^-9)5x⁴

= 54x^-5 + 5x⁴(3 - 6x^-9)

(ii) dy/dx = x^-4[0 - 4(-5x^-6)] + (3 - 4x^-5)(-4x^-5)

= 20x^-10 - 4x^-5(3 - 4x^-5)