i have a test tomorrow and i need help with some of the questions on the review. i have like 5 of them. here is the first one.
Find the derivative of the function y=xTanh^-1(lnx)
You need to use both the chain rule and the product rule.
First use the product rule:
$\displaystyle u = x \Rightarrow \frac{du}{dx} = 1$.
$\displaystyle v = \tanh^{-1} (\ln x) \Rightarrow \frac{dv}{dx} = ?$
To get $\displaystyle \frac{dv}{dx}$ you need to use the chain rule:
Let $\displaystyle w = \ln x \Rightarrow \frac{dw}{dx} = \frac{1}{x}$ and $\displaystyle v = \tanh^{-1} w$.
Then $\displaystyle \frac{dv}{dx} = \frac{dv}{dw} \cdot \frac{dw}{dx} = \, .... $
Now put it all together.