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

Problem

d()/d(x)√(5,x4)

Solution

1. Rewrite the radical expression using a fractional exponent.

√(5,x4)=x(4/5)

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

d(x(4/5))/d(x)=4/5*x(4/5−1)

3. Subtract the exponents to simplify the expression.

4/5−1=−1/5

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

4/5*x(−1/5)=4/(5*x(1/5))=4/(5√(5,x))

Final Answer

d(√(5,x4))/d(x)=4/(5√(5,x))

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