Find the Derivative - d/dx x^2-16/x

Problem

d()/d(x)*(x2−16/x)

Solution

1. Apply the sum rule for differentiation to separate the terms.

d()/d(x)*(x2−16/x)=d(x2)/d(x)−d()/d(x)16/x

2. Rewrite the second term using a negative exponent to prepare for the power rule.

d()/d(x)16/x=(d(16)*x(−1))/d(x)

3. Apply the power rule d(xn)/d(x)=n*x(n−1) to both terms.

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

(d(16)*x(−1))/d(x)=−16*x(−2)

4. Combine the results and simplify the signs.

2*x−(−16*x(−2))=2*x+16*x(−2)

5. Rewrite with positive exponents to reach the final form.

2*x+16/(x2)

Final Answer

d()/d(x)*(x2−16/x)=2*x+16/(x2)

Want more problems? Check here!