Question

Differentiate the following w.r.t.x: (1 + 4x)⁵ (3 + x −x2)⁸ 

Answer 1

Let y = (1 + 4x)⁵ (3 + x −x2)⁸  
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(1 + 4x)^5 (3 + x - x^2)^8`

= `(1 + 4x)^5."d"/"dx"(3 + x - x^2)^8 + (3 + x - x^2)^8."d"/"dx"(1 + 4x)^5`

= `(1 + 4x)^5 xx 8(3 + x - x^2)^7."d"/"dx"(3 + x - x^2) + (3 + x - x^2)^8 xx 5(1 + 4x)^4."d"/"dx"(1 + 4x)`

= 8(1 + 4x)⁵ (3 + x – x²)⁷. (0 + 1 – 2x) + 5(1 + 4x)⁴ (3 + x – x²)⁸. (0 + 4 x 1)
= 8(1 – 2x)(1 + 4x)⁵(3 + x – x²)⁷ + 20(1 + 4x)⁴(3 + x - x²)⁸.