Thread: exponential differentiation

hello, currently im studying the exponential and logarithmic differentiation and integration, and i came across this, and strangely enough i cant finish approaching it, though im on the right track, can anyone help me differentiate this please? thank you

Originally Posted by Heinsbergrelatz

hello, currently im studying the exponential and logarithmic differentiation and integration, and i came across this, and strangely enough i cant finish approaching it, though im on the right track, can anyone help me differentiate this please? thank you

use the chain rule

yes i know you have to use the chain rule, after doing:


but somehow, i cant get the correct answer..

you just need to differentiate to complete the chain.

but if we only differentiate that, we are completely ignoring the differentiating rule of the natural log function?

you need to differentiate that in conjunction with the differentiation of the natural log function. Remember, h(x)=(f(g(x)) : h'(x)=f'(g(x))g'(x)dx

yes i remeber, but the rule in my book says,




in general;
where is a function of

it's the same thing as what I wrote. u is a function, in this case . now differentiate it.

but how about the ?

you have that, and you multiply it with to complete the chain rule. That's all. and for u, chances are the quotient rule would be a good place to start.

Originally Posted by Heinsbergrelatz

yes i remeber, but the rule in my book says,




in general;
where is a function of

the end products in the first two differentiations are missing a 'dx' at the end. That could be the source of some of your confusion.

ok i get the procedure now, thank you,

o yes, by the way, does it matter in this case substantially without the "dx"?
and also what does this "dx" denote exactly?

dx is, probably oversimplifying, the derivative of x, or rather, the change of x. In most cases it's useful when dealing with x's that are functions of other variables, as a reminder to take the derivative, using the chain rule, until you are down to the most isolated variable.

oh i see, well thank you for the help,i appreciate it