Find the Derivative - d/d@VAR f(x)=(x^3+x+4)/(2x)

Problem

d()/d(x)(x3+x+4)/(2*x)

Solution

1. Simplify the expression by dividing each term in the numerator by the denominator to avoid using the quotient rule.

(x3+x+4)/(2*x)=(x3)/(2*x)+x/(2*x)+4/(2*x)

2. Reduce the powers of x in each term.

(x2)/2+1/2+2*x(−1)

3. Apply the power rule to each term individually, where d(xn)/d(x)=n*x(n−1)

d()/d(x)*(1/2*x2+1/2+2*x(−1))=1/2*(2*x)+0+2*(−1*x(−2))

4. Simplify the resulting expression.

x−2*x(−2)

5. Rewrite the expression using positive exponents.

x−2/(x2)

Final Answer

d()/d(x)(x3+x+4)/(2*x)=x−2/(x2)

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