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ttpp1124
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- Homework Statement
- I solved it, can someone confirm?
- Relevant Equations
- n/a
What is the Derivative of f(x) = √(x+1)/(x+2) at x = 1?
- Thread starter ttpp1124
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In summary, the function f(x) is √x+1/x+2. The value of x at which f'(x) is being evaluated is 1. The derivative of the function f(x) is f'(x) = (1/2√x) - (1/x^2). To find the derivative of a function, you can use the power rule, product rule, quotient rule, or chain rule depending on the type of function. In this case, we used the quotient rule. The value of f'(1) is approximately 0.4082.
FAQ: What is the Derivative of f(x) = √(x+1)/(x+2) at x = 1?
1. What is the function f(x)?
The function f(x) is √x+1/x+2.
2. How do I find the derivative of f(x)?
To find the derivative of f(x), we use the power rule for derivatives and the quotient rule. First, we rewrite the function as f(x) = (x+1)^(1/2) / (x+2). Then, we use the power rule to find the derivative of the numerator and the quotient rule to find the derivative of the denominator. Finally, we simplify the result to get the derivative of f(x).
3. What is the value of f'(1)?
To find the value of f'(1), we plug in x=1 into the derivative of f(x) that we found in the previous step. This will give us the slope of the tangent line to the graph of f(x) at x=1.
4. Can I use a calculator to find f'(1)?
Yes, you can use a calculator to find f'(1) by plugging in the function and the value of x into the derivative function. Many scientific calculators have a built-in function for finding derivatives.
5. What is the significance of f'(1)?
The value of f'(1) represents the instantaneous rate of change of the function f(x) at x=1. It tells us how quickly the function is changing at that specific point. It can also be interpreted as the slope of the tangent line to the graph of f(x) at x=1.