Question

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)

Answer 1

Refer to the photo attached.

Answer 2

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`