1) Differentiate the following using the product rule or the quotient rule.. (i) y=(x^2 - 1)(x^3 + 3) (ii) y=x^5 (3x^2+ 4x-7)

Question

asked Oct 18, 2023 211k views

2 Answers

Pierrotlefou · Answer 1 · 2023-10-23T22:34:17+0000

Answer:

Explanation:

1) y=(x^2 - 1)(x^3 + 3)

From the product rule with u = x^2 - 1 and v = x^3, we find

$(d)/(dx) {(x^2-1)(x^3+3)=(x^2-1)(d)/(dx) (x^3+3)+(x^3+3)(d)/(dx) (x^2-1)\\$

(x^2-1)(3x^2)+(x^3+3)(2x)

$=3x^4-3x^2+2x^4+6x\\=5x^4-3x^2+6x$

2) y=x^5 (3x^2+ 4x-7)

--->
21x^6+24x^5-35x^4