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