Find the Derivative - d/dx cube root of x^4

Problem

d(√(3,x4))/d(x)

Solution

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

√(3,x4)=x(4/3)

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

d(x(4/3))/d(x)=4/3*x(4/3−1)

3. Simplify the exponent by performing the subtraction.

4/3−1=4/3−3/3=1/3

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

4/3*x(1/3)=(4√(3,x))/3

Final Answer

d(√(3,x4))/d(x)=(4√(3,x))/3

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