Find the Derivative - d/dx y=x^(1/3)

Problem

d()/d(x)*x(1/3)

Solution

1. Identify the function as a power function of the form xn where n=1/3

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

3. Substitute the value of n into the power rule formula.

d(x(1/3))/d(x)=1/3*x(1/3−1)

4. Simplify the exponent by performing the subtraction 1/3−1=−2/3

d(x(1/3))/d(x)=1/3*x(−2/3)

5. Rewrite the expression using positive exponents if desired.

d(x(1/3))/d(x)=1/(3*x(2/3))

Final Answer

d(x(1/3))/d(x)=1/(3*x(2/3))

Want more problems? Check here!