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If y = sqrt(x^2 + 1), find dy/dx at x = 0.
If y = sqrt(x^2 + 1), find dy/dx at x = 0.
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Practice Questions
1 question
Q1
If y = sqrt(x^2 + 1), find dy/dx at x = 0.
0
1
1/2
1/√2
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dy/dx = (1/2)(x^2 + 1)^(-1/2)(2x). At x = 0, dy/dx = (1/2)(1)^(-1/2)(0) = 0.
Questions & Step-by-step Solutions
1 item
Q
Q: If y = sqrt(x^2 + 1), find dy/dx at x = 0.
Solution:
dy/dx = (1/2)(x^2 + 1)^(-1/2)(2x). At x = 0, dy/dx = (1/2)(1)^(-1/2)(0) = 0.
Steps: 8
Show Steps
Step 1: Start with the equation y = sqrt(x^2 + 1).
Step 2: Rewrite the square root as a power: y = (x^2 + 1)^(1/2).
Step 3: Use the power rule and chain rule to find the derivative dy/dx.
Step 4: The derivative of (x^2 + 1)^(1/2) is (1/2)(x^2 + 1)^(-1/2) * (derivative of x^2 + 1).
Step 5: The derivative of x^2 + 1 is 2x, so we have dy/dx = (1/2)(x^2 + 1)^(-1/2)(2x).
Step 6: Simplify the expression: dy/dx = (x)(x^2 + 1)^(-1/2).
Step 7: Now, substitute x = 0 into the derivative: dy/dx = (0)(1)^(-1/2).
Step 8: Calculate the result: dy/dx = 0.
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