Differentiate 1-xrootx /1+xrootx
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Secondary School Math 5 points
Differentiate (x+1/x)(rootx+1/rootx)
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revanth20031
revanth20031 Ambitious
y' = 1/(2(x - 1)^(1/2)) + 1/(2(x + 1)^(1/2))
Explanation:
We will have to apply the chain rule twice to this problem.
Step 1: Determine the derivative of y = sqrt(x - 1)
Let y = u^(1/2) and u = x - 1
Then dy/dx = 1/2u^(-1/2) xx 1 = 1/(2(x - 1)^(1/2))
Step 2: Determine the derivative of y = sqrt(x + 1)
Let y = u^(1/2) and u = x+ 1#
Then dy/dx = 1/2u^(-1/2) xx 1 = 1/(2(x + 1)^(1/2))
Step 3: Combine the two derivatives using the sum rule
y' = 1/(2(x - 1)^(1/2)) + 1/(2(x + 1)^(1/2))