# How do you differentiate #f(x) = sqrt(arctan(3x) # using the chain rule?

##### 1 Answer

Chain rule says that

Here we have three functions that are

We start from the most "external" that is the square root

We know that

then, applying the chain rule we have

We have now to calculate the derivative of

We know that

then we reapply the chain rule

and finally the easy one

We substitute everything back and write