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

Problem

d()/d(x)√(4,x)

Solution

1. Rewrite the radical expression using a fractional exponent to make it easier to differentiate.

√(4,x)=x(1/4)

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

d(x(1/4))/d(x)=1/4*x(1/4−1)

3. Subtract the exponents to simplify the expression.

1/4−1=−3/4

1/4*x(−3/4)

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

1/(4*x(3/4))=1/(4√(4,x3))

Final Answer

d(√(4,x))/d(x)=1/(4√(4,x3))

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