Natural log problem

**~berserk** · November 13th 2012, 09:00 PM

Differentiate: h(t)= ln((t^2+1)/(t+1))

I'm having some trouble with this one. Not sure if I am doing too much work for it.

Also this one: y= x^x^2

Do I have to use logarithmic differentiaton for the second?

**MarkFL** · November 13th 2012, 09:13 PM

For the second one, another option besides logarithmic differentiation is exponential differentiation:

$y=x^{x^2}=e^{\ln\left(x^{x^2} \right)}=e^{x^2\ln(x)}$

Now use the exponential, chain and product rules to find the derivative.

**~berserk** · November 13th 2012, 09:16 PM

would you be able to show me how to differentiate it logarithmically?

**MarkFL** · November 13th 2012, 09:28 PM

We are given to differentiate:

$y=x^{x^2}$

Take the natural log. of both sides:

$\ln(y)=\ln\left(x^{x^2} \right)=x^2\ln(x)$

Now, implicitly differentiate both sides with respect to $x$ . I don't want to just work out the whole thing, but I will help guide you if you get stuck.

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