Find the Derivative - d/dx fifth root of x^6

Problem

d()/d(x)√(5,x6)

Solution

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

√(5,x6)=x(6/5)

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

d(x(6/5))/d(x)=6/5*x(6/5−1)

3. Simplify the exponent by performing the subtraction.

6/5−1=6/5−5/5=1/5

4. Write the final derivative in radical form if desired.

6/5*x(1/5)=(6√(5,x))/5

Final Answer

d(√(5,x6))/d(x)=(6√(5,x))/5

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