Find the Derivative - d/dx (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 the quotient rule.

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

2. Reduce the powers of x and rewrite the terms using negative exponents where necessary.

1/2*x2+1/2+2*x(−1)

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

d()/d(x)1/2*x2=x

d()/d(x)1/2=0

d()/d(x)*2*x(−1)=−2*x(−2)

4. Combine the results and rewrite the negative exponent as a fraction.

x−2/(x2)

5. Find a common denominator to express the final result as a single fraction.

(x3−2)/(x2)

Final Answer

d()/d(x)(x3+x+4)/(2*x)=(x3−2)/(x2)

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