Find the Derivative - d/dx sixth root of x^7

Problem

d(√(6,x7))/d(x)

Solution

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

√(6,x7)=x7/6

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

d(x7/6)/d(x)=7/6*x(7/6−1)

3. Simplify the exponent by performing the subtraction.

7/6−1=7/6−6/6=1/6

4. Rewrite the result back into radical form if desired.

7/6*x1/6=(7√(6,x))/6

Final Answer

d(√(6,x7))/d(x)=(7√(6,x))/6

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