Find the Derivative - d/dx 2/( square root of x)

Problem

d()/d(x)2/√(,x)

Solution

1. Rewrite the expression using exponents to make it easier to differentiate.

2/√(,x)=2*x(−1/2)

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

(d(2)*x(−1/2))/d(x)=2⋅(−1/2)*x(−1/2−1)

3. Simplify the coefficient and the exponent.

2⋅(−1/2)=−1

−1/2−1=−3/2

4. Rewrite the result back into radical form with a positive exponent.

−x(−3/2)=−1/(x(3/2))

−1/(x(3/2))=−1/√(,x3)

Final Answer

d()/d(x)2/√(,x)=−1/(x√(,x))

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