Find the Derivative - d/dx fifth root of x^2

Problem

d()/d(x)√(5,x2)

Solution

1. Rewrite the radical expression using a rational exponent by applying the rule √(n,xm)=x(m/n)

√(5,x2)=x(2/5)

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

d(x(2/5))/d(x)=2/5*x(2/5−1)

3. Subtract the exponents to simplify the expression.

2/5*x(−3/5)

4. Rewrite the expression with a positive exponent using the rule x(−n)=1/(xn)

2/(5*x(3/5))

5. Convert the rational exponent back into radical form using the rule x(m/n)=√(n,xm)

2/(5√(5,x3))

Final Answer

d(√(5,x2))/d(x)=2/(5√(5,x3))

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