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

Problem

d()/d(x)√(4,x3)

Solution

1. Rewrite the radical expression using a rational exponent.

√(4,x3)=x(3/4)

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

d(x(3/4))/d(x)=3/4*x(3/4−1)

3. Subtract the exponents to simplify the expression.

3/4−1=−1/4

4. Simplify the result by moving the negative exponent to the denominator and converting back to radical form.

3/4*x(−1/4)=3/(4*x(1/4))=3/(4√(4,x))

Final Answer

d(√(4,x3))/d(x)=3/(4√(4,x))

Want more problems? Check here!