Find the Derivative - d/dx (x^3+5)/x

Problem

d()/d(x)(x3+5)/x

Solution

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

(x3+5)/x=(x3)/x+5/x

2. Rewrite the terms using exponent notation to prepare for the power rule.

x2+5*x(−1)

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

d(x2)/d(x)+(d(5)*x(−1))/d(x)

4. Calculate the derivatives of the individual terms.

2*x+5*(−1)*x(−2)

5. Simplify the resulting expression by moving the negative exponent back to the denominator.

2*x−5/(x2)

Final Answer

d()/d(x)(x3+5)/x=2*x−5/(x2)

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