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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.
What is the second derivative of x raised to the 1 divided by x?
To calculate the derivate of a power, where both the base and the exponent are functions of x, requires a technique called logarithmic derivation. I'll leave the details to you; it is not particularly difficult. You can look up "logarithmic differentiation" in the Wikipedia for some examples.
What is the difference in the Natural Logarithmic Function and the Common Logarithmic Function?
Natural logarithms use base e (approximately 2.71828), common logarithms use base 10.
Use of probability in logarithmic relations?
None. If you have an exact relationship - whether it is linear, polynomial, logarithmic or whatever - probability has no role to play.
What are the three laws of logarithmic?
There is no subject to this question: "logarithmic" is an adjective but there is no noun (or noun phrase) to go with it. The answer will depend on logarithmic what? Logarithmic distribution, logarithmic transformation or what?
What type of scale does a Richter scale use?
a logarithmic scale
When would you not use logarithmic scale?
When dealing with farm animals
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
Differentiation formulas of mathematics d dx x x plus 9?
If you mean x squared + 9, you differentiate this as follows: Use the differentiation formula for a power, to differentiate the x squared. Separately, use the differentiation formula for a constant, to differentiate the 9. Finally, use the differentiation formula for a sum to add up the parts.
What is a real world use of a logarithmic scale?
One of them is measuring earthquakes.
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.
Why would one need to use implicit differentiation?
Implicit differentiation is a special case of the well-known rules of derivatives. Using implicit differentiation would be beneficial in math equations.
