Find the Derivative - d/dx fourth root of x^3

Problem

d(√(4,x^3))/d(x)

Solution

1. Rewrite the radical expression using a rational exponent. The fourth root of x^3 is equivalent to x raised to the power of the inside exponent divided by the root index.

√(4,x^3)=x^(3/4)

2. Apply the power rule for differentiation, which states that d(x^n)/d(x)=n*x^(n−1) Here, n=3/4

d(x^(3/4))/d(x)=3/4*x^(3/4−1)

3. Simplify the exponent by performing the subtraction.

3/4−1=−1/4

4. Rewrite the expression with a positive exponent by moving the variable to the denominator.

3/4*x^(−1/4)=3/(4*x^(1/4))

5. Convert the rational exponent back into radical form.

3/(4*x^(1/4))=3/(4√(4,x))

Final Answer

d(√(4,x^3))/d(x)=3/(4√(4,x))

Want more problems? Check here!