Find the Derivative - d/dx square root of x

Problem

d(√(,x))/d(x)

Solution

1. Rewrite the square root as a power using the rule √(,x)=x(1/2)

d(√(,x))/d(x)=d(x(1/2))/d(x)

2. Apply the power rule for derivatives, which states d(xn)/d(x)=n*x(n−1) where n=1/2

d(x(1/2))/d(x)=1/2*x(1/2−1)

3. Simplify the exponent by performing the subtraction 1/2 - 1 = -1/2$.

1/2*x(1/2−1)=1/2*x(−1/2)

4. Convert the negative exponent back into a radical form using the rules x(−n)=1/(xn) and x(1/2)=√(,x)

1/2*x(−1/2)=1/(2√(,x))

Final Answer

d(√(,x))/d(x)=1/(2√(,x))

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