Hi I am fine when it comes to straightforward differntiation but when its composite I mean when you have to apply say product rule and then chain rule etc. I really haven't got a clue when to proceed with second rule. I have a problem here and I will really appriciate it if someone can explain in details:
f(x)=e^(6x) sq.rt.(1+3x^2) I don't know how to use fancy text but this should read
f(x) = e to the power of 6x multiplied by square root of 1 plus 3x squared.
I know you apply prodcut and then composite rule- but I get stuck as soon as I did prodcut rule. if someone can illustarte the whole process and logic that will make my life easier
Wasn't able to open that, but...
Just in case a picture helps...
... where (key in spoiler) ...
Spoiler:
Spoiler:
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!
What you're missing there is the 6x in the bottom-right corner of my diagrams. (Arising from the chain rule for differentiation, just as the 6 popped out from inside the exponential - you included that one, just do the same on the right, as per the diagram.)
PS the third (or fourth) balloon along has the sqrt tweaked into a fraction to prepare for simplifying.
You just need a bit more co-ordination.
On the attachment, you wrote
This is in fact "v" written in "index form" in preparation for differentiation.
You correctly differentiated
using the Chain Rule.
To differentiate "v"
Writing the stages in this way helps simplify the Chain Rule calculations.