Question

Differentiate x² logx

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Answer 1

༒࿐៚ Answer ༒࿐៚

What is the derivative of x^2 log x?

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.