Home > Calculus > Differentiating Logarithmic Functions with Base e

What is the derivative of #lnx/x^2#?

Answer 1

Emily Ammerman

#f'(x)=(1-lnx^2)/x^3#

use the quotient rule, which should be memorised.

#f(x)=u/v" "=>" "f'(x)=(vu'-uv')/v^2#

#f(x)=(lnx)/x^2#

#u=lnx=>u'=1/x#

#v=x^2=>v'=2x#

#f'(x)=(x^2xx1/x-2xlnx)/(x^2)^2#

#f'(x)=(x-2xlnx)/x^4=(x(1-2lnx))/x^4=(cancel(x)(1-lnx^2))/(cancel(x^4)x^3)#

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Answer 2

Paisley Johnson

The derivative of ln(x)/x^2 is (1 - 2ln(x))/x^3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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