Find the Derivative - d/d@VAR f(x)=x^(1/4)

Problem

d()/d(x)*x(1/4)

Solution

1. Identify the function as a power function of the form ƒ(x)=xn where n=1/4

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

3. Substitute the value of n into the power rule formula.

d(x(1/4))/d(x)=1/4*x(1/4−1)

4. Simplify the exponent by performing the subtraction 1/4−4/4=−3/4

d(x(1/4))/d(x)=1/4*x(−3/4)

5. Rewrite the expression using positive exponents if desired, moving the term to the denominator.

d(x(1/4))/d(x)=1/(4*x(3/4))

Final Answer

d(x(1/4))/d(x)=1/(4*x(3/4))

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