Find the Derivative - d/dx

Problem

d()/d(x)*(√(,x)−1/√(,x))

Solution

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

y=x(1/2)−x(−1/2)

2. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1) to each term individually.

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

3. Simplify the exponents by performing the subtraction.

d(y)/d(x)=1/2*x(−1/2)+1/2*x(−3/2)

4. Convert the expression back into radical form and positive exponents for the final result.

d(y)/d(x)=1/(2√(,x))+1/(2√(,x3))

Final Answer

d()/d(x)*(√(,x)−1/√(,x))=1/(2√(,x))+1/(2*x√(,x))

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