# Math Help - Help! Test tomorrow.

1. ## 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)

2. 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:

$u = x \Rightarrow \frac{du}{dx} = 1$.

$v = \tanh^{-1} (\ln x) \Rightarrow \frac{dv}{dx} = ?$

To get $\frac{dv}{dx}$ you need to use the chain rule:

Let $w = \ln x \Rightarrow \frac{dw}{dx} = \frac{1}{x}$ and $v = \tanh^{-1} w$.

Then $\frac{dv}{dx} = \frac{dv}{dw} \cdot \frac{dw}{dx} = \, ....$

Now put it all together.