question_answer 86)

Diff. (x2 – 5x + 8) (x3 + 7x + 9) by (i) product rule (ii) expanding the product to obtain a single polynomial. (iii) logarithmic differentiation. Do they give the same answer ?  

Answer:

(i) Let y = (x2 ? 5x + 8) (x3 + 7x + 9)                               + (x3 + 7x ? 9) (2x ? 5)       = 3x4 + 7x2 ? 15x3 ? 35x + 24x2 + 56 + 2x4       ?5x3 + 14x2 ?35x + 18x ? 45             (ii) Let y = (x2 ? 5x + 8) (x3 + 7x + 9)       =x5 ? 5x4 + 15x3 ? 26x2 + 11x + 72             (iii) Let y = (x2 ? 5x + 8) (x3 + 7x + 9)                               Diff.w.r.t. x                                                                                     Hence in all the three cases, we have the same answer.