# How do you differentiate #(3x^2+4) / (sqrt(1+x^2))#?

##### 1 Answer

Hey there! :)

Looks tough when you first see it, right? However, differentiation rules are like super powers.

Here is the short story:

Now for the far more exciting long story:

The quotient rule says that if we have two differentiable functions, say

So now we just apply this!

So,

Now we have to use a few super powers here. The power rule and chain rule are part of our arsenal.

I hope it is clear that

(If not, just shout!) - We just applied the power rule to the first term and the second term is a constant. And constants don't stand a chance against differentiation! They just become zero.

Next, we harness the power of the chain rule, that says for any differentiable functions, say,

We apply it (here u is the square root function and h(x) = (1+x^2)):

Finally, plugging these things back in their rightful place, we get