Find the Derivative - d/dx seventh root of x

Problem

d(√(7,x))/d(x)

Solution

1. Rewrite the radical expression using a fractional exponent.

√(7,x)=x(1/7)

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

d(x(1/7))/d(x)=1/7*x(1/7−1)

3. Subtract the exponents to simplify the expression.

1/7−1=−6/7

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

1/7*x(−6/7)=1/(7*x(6/7))

Final Answer

d(√(7,x))/d(x)=1/(7*x(6/7))

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