Find the Derivative - d/dx fourth root of x

Problem

d(√(4,x))/d(x)

Solution

1. Rewrite the radical expression as a power using the rule √(n,xm)=xm/n

√(4,x)=x1/4

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

d(x1/4)/d(x)=1/4*x(1/4−1)

3. Subtract the exponents to simplify the expression.

1/4−1=−3/4

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

1/4*x(−3/4)=1/(4*x3/4)

1/(4*x3/4)=1/(4√(4,x3))

Final Answer

d(√(4,x))/d(x)=1/(4√(4,x3))

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