Find the Derivative - d/dx (x^3)/3+1/(4x)

Problem

d()/d(x)*((x3)/3+1/(4*x))

Solution

1. Rewrite the expression using power notation to make differentiation easier.

(x3)/3+1/4*x(−1)

2. Apply the sum rule for derivatives, which allows for differentiating each term independently.

d()/d(x)(x3)/3+d()/d(x)1/4*x(−1)

3. Apply the power rule d(xn)/d(x)=n*x(n−1) to the first term.

1/3⋅3*x2=x2

4. Apply the power rule to the second term.

1/4⋅(−1)*x(−2)=−1/(4*x2)

5. Combine the results of the differentiated terms.

x2−1/(4*x2)

Final Answer

d()/d(x)*((x3)/3+1/(4*x))=x2−1/(4*x2)

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