Find the Derivative - d/dx 1/(x^(1/2))

Problem

d()/d(x)1/(x(1/2))

Solution

1. Rewrite the expression using negative exponents to prepare for the power rule.

1/(x(1/2))=x(−1/2)

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

d(x(−1/2))/d(x)=−1/2*x(−1/2−1)

3. Simplify the exponent by performing the subtraction.

−1/2*x(−3/2)

4. Rewrite the expression using positive exponents and radical notation if desired.

−1/(2*x(3/2))

Final Answer

d()/d(x)1/(x(1/2))=−1/(2*x(3/2))

Want more problems? Check here!