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

Problem

d()/d(x)4/√(3,x)

Solution

1. Rewrite the expression using exponents to make it easier to differentiate.

4/√(3,x)=4/(x(1/3))

2. Apply the rule for negative exponents to move the variable to the numerator.

4*x(−1/3)

3. Use the power rule, which states that d(xn)/d(x)=n*x(n−1) and the constant multiple rule.

(d(4)*x(−1/3))/d(x)=4⋅(−1/3)*x(−1/3−1)

4. Simplify the exponent and the coefficient.

−4/3*x(−4/3)

5. Convert the expression back into radical form with a positive exponent.

−4/(3*x(4/3))=−4/(3√(3,x4))

Final Answer

d()/d(x)4/√(3,x)=−4/(3*x√(3,x))

Want more problems? Check here!