Find the Derivative - d/dx 1/( square root of x^9)

Problem

d()/d(x)1/√(,x9)

Solution

1. Rewrite the expression using exponent rules to prepare for differentiation.

1/√(,x9)=1/(x(9/2))

2. Apply the rule for negative exponents to move the term to the numerator.

x(−9/2)

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

d(x(−9/2))/d(x)=−9/2*x(−9/2−1)

4. Simplify the exponent by performing the subtraction.

−9/2*x(−11/2)

5. Convert the expression back into radical form with a positive exponent.

−9/(2*x(11/2))=−9/(2√(,x11))

Final Answer

d()/d(x)1/√(,x9)=−9/(2*x(11/2))

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