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Question
Differentiate the following w.r.t.x. :
y = log ex3 log x3
Sum
Solution
Let y = (log ex3) (log x3) = (x3 log e)(log x3)
= x3 log x3 ...[∵ log e = 1]
= x3 (3 log x)
= 3x3 log x
∴ `("d"y)/("d"x) = "d"/("d"x) [3x^3 log x]`
= `3"d"/("d"x) (x^3 log x)`
= `3[x^3 "d"/("d"x) (log x) + (log x) "d"/("d"x) (x^3)]`
= `3[x^3 (1/x) + (log x)(3x^2)]`
= 3x2 + 9x2 log x
= 3x2 (1 + 3 log x)
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Derivative of Logarithmic Functions
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Chapter 9: Differentiation - Exercise 9.2 [Page 192]
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