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Here we must use the product rule to differeniate because x appears in both terms of the equation, therefore both parts must be differentiated. So we will set u= x² and v= (5x-1)^(1/2) written ...

The best way to answer these kind of questions is by moving all the unknowns to one side. In this case, the only unknown is x, so we should start by moving all the x's to one side. Since there are 4x's on...

To find the derivative of two functions multiplied by each other we would use the product rule.

The product rule: (fg)'(x) = f '(x).g(x) + f(x).g'(x)

First we need to split our function into...

 To differentiate this function we use the product rule. In the product rule we, leave the first alone, differentiate the second, and leave the second alone, differentiate the first.                      ...

The square of 5 is 25 and the square of 7 is 49. The prime numbers found between these 2 values are: 29, 31, 37, 41, 43 and 47. This means the smallest value fitting the criteria is 29 and the largest val...