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