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?
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?
For the second one, another option besides logarithmic differentiation is exponential differentiation:
$\displaystyle y=x^{x^2}=e^{\ln\left(x^{x^2} \right)}=e^{x^2\ln(x)}$
Now use the exponential, chain and product rules to find the derivative.
We are given to differentiate:
$\displaystyle y=x^{x^2}$
Take the natural log. of both sides:
$\displaystyle \ln(y)=\ln\left(x^{x^2} \right)=x^2\ln(x)$
Now, implicitly differentiate both sides with respect to $\displaystyle x$. I don't want to just work out the whole thing, but I will help guide you if you get stuck.