SOLUTION: Use the method of Differentiation from first principle to prove that the
derivative of the square root of x is given below.
(d/dx) sqr r of x = 1/2sqrr of x
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Question 1164542: Use the method of Differentiation from first principle to prove that the
derivative of the square root of x is given below.
(d/dx) sqr r of x = 1/2sqrr of x
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
In order to compute the derivative from first principles, we need to determine the following:
lim(h->0)[(sqrt(x+h) - sqrt(x))/h]
Rationalize the numerator by multiplying top and bottom by sqrt(x+h) + sqrt(x).
This gives lim(h->0)[(x+h - x)/(h*(sqrt(x+h) + sqrt(x)))]
This reduces to lim(h->0)[1/(sqrt(x+h) + sqrt(x))]
Letting h go to zero, we get 1/(2*sqrt(x))
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