Find the Derivative - d/dx fourth root of x^5

Problem

d(√(4,x5))/d(x)

Solution

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

√(4,x5)=x5/4

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

d(x5/4)/d(x)=5/4*x(5/4−1)

3. Simplify the exponent by performing the subtraction.

5/4−1=5/4−4/4=1/4

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

5/4*x1/4=(5√(4,x))/4

Final Answer

d(√(4,x5))/d(x)=(5√(4,x))/4

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