Find the Derivative - d/dx 11 root of x

Problem

d()/d(x)√(11,x)

Solution

1. Rewrite the radical expression as a power with a fractional exponent using the rule √(n,x)=x(1/n)

√(11,x)=x(1/11)

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

d(x(1/11))/d(x)=1/11*x(1/11−1)

3. Subtract the exponents by finding a common denominator.

1/11−1=1/11−11/11=−10/11

4. Simplify the expression by moving the negative exponent to the denominator.

1/11*x(−10/11)=1/(11*x(10/11))

Final Answer

d(√(11,x))/d(x)=1/(11*x(10/11))

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