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Question
Differentiate the following w.r.t.x:
(x2 + 4x + 1)3 + (x3− 5x − 2)4
Solution
Let y = (x2 + 4x + 1)3 + (x3− 5x − 2)4
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[(x^2 + 4x + 1)^3 + (x^3 - 5x - 2)^4]`
`= "d"/"dx"(x^2 + 4x + 1)^3 + "d"/"dx"(x^3 - 5x - 2)^4`
`= 3(x^2 + 4x + 1)^2."d"/"dx"(x^2 + 4x + 1) + 4(x^3 - 5x - 2)^3. "d"/"dx"(x^3 - 5x - 2)`
= 3(x2 + 4x + 1)2. (2x + 4 × 1 + 0) + 4(x3 – 5x – 2)3. (3x2 – 5 × 1 – 0)
= 3(2x + 4)(x2 + 4x + 1)2 + 4(3x2 – 5)(x3 – 5x – 2)3
= 3 × 2(x + 2)(x2 + 4x + 1)2 + 4(3x2 – 5)(x3 – 5x – 2)3
= 6(x + 2)(x2 + 4x + 1)2 + 4(3x2 – 5)(x3 – 5x – 2)3
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