Evaluate the Derivative at @POINT square root of x , (1,1)

Problem

d(√(,x))/d(x)* at *(1,1)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=√(,x)

2. Rewrite the square root as an exponent to make it easier to apply the power rule: ƒ(x)=x(1/2)

3. Apply the power rule for derivatives, which states d(xn)/d(x)=n*x(n−1)

4. Calculate the derivative: d(x(1/2))/d(x)=1/2*x(−1/2)

5. Simplify the expression by moving the negative exponent to the denominator: 1/(2√(,x))

6. Substitute the xcoordinate from the point (1,1) into the derivative: 1/(2√(,1))

7. Evaluate the final numerical value: 1/(2*(1))=1/2

Final Answer

d(√(,x))/d(x)|=1/2

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