Question

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

(i) y = (x³ + x² + 1)sinx

(ii) y = (x² - 5x + 6)secx

Answer 1

(i) dy/dx = (x³ + x² + 1)d/dx sinx + sinx d/dx(x³ + x² + 1)

= (x³ + x² + 1)cosx + (3x² + 2x)sinx

(ii) dy/dx = (x² - 5x + 6)d/dx(secx) + sec. d/dx(x² - 5x + 6)

= (x² - 5x + 6)secxtanx + secx.(2x - 5)