if y=x^2 log x find dy/dx
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Answer:
What is the derivative of x^2 log x?
Solution: Let y = x^2 log x
log y = log x^2 + log (log x)
(1/y).dy/dx = 2x/x^2 + (1/log x).(1/x)
= 2/x + 1/(x log x), or
dy/dx = y [2/x + 1/(x log x)], or
= (y/x) [2 + 1/log x], or
= (x^2 log x)/x*[2 + 1/log x], or
= x log x*[2 + 1/log x], or
= 2x log x + x, or
= x[2 log x + 1}. Answer.
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