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Question
Find `"dy"/"dx"` if, y = log(10x4 + 5x3 - 3x2 + 2)
Solution
y = log(10x4 + 5x3 - 3x2 + 2)
Differentiating both sides w.r.t.x, we get
`"dy"/"dx" = "d"/"dx"[log (10"x"^4 + 5"x"^3 - 3"x"^2 + 2)]`
`= 1/(10"x"^4 + 5"x"^3 - 3"x"^2 + 2) * "d"/"dx" (10"x"^4 + 5"x"^3 - 3"x"^2 + 2)`
`= 1/(10"x"^4 + 5"x"^3 - 3"x"^2 + 2) * [10(4"x"^3) + 5(3"x"^2) - 3(2"x") + 0]`
∴ `"dy"/"dx" = (40"x"^3 + 15"x"^2 - 6"x")/(10"x"^4 + 5"x"^3 - 3"x"^2 + 2)`
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