Find the Derivative - d/dx y=(x^2-1)/(x^3)

Problem

d()/d(x)(x2−1)/(x3)

Solution

1. Rewrite the expression by splitting the fraction into two separate terms to avoid using the quotient rule.

(x2−1)/(x3)=(x2)/(x3)−1/(x3)

2. Simplify the terms using the laws of exponents.

(x2)/(x3)−1/(x3)=x(−1)−x(−3)

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

d()/d(x)*(x(−1)−x(−3))=−1*x(−2)−(−3*x(−4))

4. Simplify the signs and the coefficients.

−x(−2)+3*x(−4)

5. Rewrite the expression with positive exponents to match the original fractional form.

−1/(x2)+3/(x4)

6. Find a common denominator to combine the terms into a single fraction.

−(x2)/(x4)+3/(x4)=(3−x2)/(x4)

Final Answer

d()/d(x)(x2−1)/(x3)=(3−x2)/(x4)

Want more problems? Check here!