Find the Derivative - d/dx y=(x^2-4)/x

Problem

d()/d(x)(x2−4)/x

Solution

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

(x2−4)/x=(x2)/x−4/x

2. Rewrite the terms using power notation to prepare for differentiation.

x−4*x(−1)

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

d(x)/d(x)−(d(4)*x(−1))/d(x)

4. Calculate the derivatives of the individual terms.

1−4*(−1)*x(−2)

5. Simplify the resulting expression by multiplying the constants and converting the negative exponent back into a fraction.

1+4*x(−2)

1+4/(x2)

6. Combine the terms into a single fraction by finding a common denominator.

(x2)/(x2)+4/(x2)

(x2+4)/(x2)

Final Answer

d()/d(x)(x2−4)/x=(x2+4)/(x2)

Want more problems? Check here!