# Help! Test tomorrow.

• Dec 2nd 2008, 12:42 PM
BigPapa
Help! Test tomorrow.
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)
• Dec 2nd 2008, 06:47 PM
mr fantastic
Quote:

Originally Posted by BigPapa
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.