Jun 28, 2015 · Note, however, that this assumes that $\ln x$ is differentiable. (That is required if you want to use the chain rule) So unless you have proved that $\ln x$ is differentiable, this proof cannot …

Jul 19, 2015 · Using the continuity of $\ln$ you can take the limit inside the logarithm.

May 20, 2020 · I have the following question: What is the intuition behind why the derivative of ln(cx) ln (c x) always equals 1/x 1 / x, for any c> 0 c> 0? I understand how to prove that algebraically using …

Nov 27, 2011 · I'm currently taking Calculus. I'm pretty good with derivatives apart from when it comes to logarithmic differentiation etc. Here is one I'm having problems with, if anyone could help that would be

May 30, 2023 · When we get the antiderivative of 1/x we put a absolute value for Ln|x| to change the domain so the domains are equal to each other. But my question is then why do we not do this for …

I thought I was supposed to make it into x(lnx) x (ln x) which should be equivalent to the original term. Then the differentiation should be easy for most people from here. 1(lnx)+x(1 x) 1 (ln x) + x (1 x) or …

Apr 6, 2018 · That said, this is a strange exercise. Presumably you have defined $\ln$ as the inverse of exponentiation, so that $$ \exp (\ln (x)) = x . $$ Then the formula for the derivative of $\ln$ follows …

Prove that the derivative of $\ln x$ is $\frac1x$ for $x≠0$ Proof : Suppose $x>0$ and write $f (x)=ln⁡〖 x〗$ in the equivalent from $x=e^ {f (x)}$ Differentiating both sides of the equation w...

May 22, 2013 · Show that $$ \frac {d} {dx} a^x = a^x \ln a. $$ How would I do a proof for this. I can't seem to get it to work anyway I try. I know that $$ \frac {d} {dx} e^x = e^x. $$ Does that help me here?

Aug 30, 2020 · I was reading about the derivative of $\ln (x)$ using chain rule.But it requires you to know $\ln (x)$ is differentiable.Then i saw the derivative of $\ln (x)$ using limit definition of derivative but...