Question

Find the derivative of the function

y=ln(7+x^2)

This is my first time doing these kind of problems so please walk me through it step by step!

Answer 1

recall that the derivative of y = ln(x)
is y' = 1/x

So, if y = ln(u), the Chain Rule says that
y' = 1/u u'

So, if we have
y = ln(7+x^2)
y' = 1/(7+x^2) * (2x) = 2x/(7+x^2)

It's just a new rule; the old methods still apply as usual. Don't forget the chain rule, product rule, quotient rule, etc.

Now you have formulas for powers, sin/cos, and logs. Next will come exponentials. And that's about all there really is.