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I take this to be y = xex.
Proceeding formally (ie, without regard to restrictions on the domain of ln x):
- Take natural logarithms of 'both sides' of above equation: ln y = ln x + x
- Implicit differentiation: y'/y = 1/x + 1
- Multiply both sides by y: y' = y ( 1/x + 1 )
- Replace y by its definition as a function: y' = xex ( 1/x + 1 ).
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What are some applications of differentiation in real life?
Yes if it was not practical it was not there. You can see the real life use on this link http://www.intmath.com/Applications-differentiation/Applications-of-differentiation-intro.php
What is the Relationship between chain rule and implicit differentiation?
Chain rule is a differentiation technique which can be used in either implicit or explicit differentiation, depending upon the problem. On the other hand, implicit differentiation is a differentiation technique, which is used when all x's and y's are on the same side. Example: x squared + y squared = 4xy, in this case, you use implicit differentiation to actually differentiate the equation, and you use the chain rule to differentiate 4xy.
Who invented differentiation?
Differentiation was invented by both Newton and Leibniz independently from one another but we commonly use Leibniz notation.
What is the relationship between exponential and logarithmic functions?
Exponential and logarithmic functions are inverses of each other.
How do you deal with differentiation in Calculus?
You learn the rules for differentiating polynomials, products, quotients, etc. Then you learn the chain rule and a couple of other rules and you're good to go for the basics. You can check your results by learning to use wolframalpha.com.
