Find the Derivative - d/dx 8/(3x^2)

Problem

d()/d(x)8/(3*x2)

Solution

1. Rewrite the expression using a negative exponent to make it easier to differentiate.

8/(3*x2)=8/3*x(−2)

2. Apply the constant multiple rule by moving the constant coefficient outside the derivative.

d()/d(x)8/3*x(−2)=8/3d(x(−2))/d(x)

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

8/3d(x(−2))/d(x)=8/3*(−2*x(−3))

4. Multiply the constants and simplify the expression.

8/3*(−2*x(−3))=−16/3*x(−3)

5. Rewrite the result with a positive exponent by moving the variable back to the denominator.

−16/3*x(−3)=−16/(3*x3)

Final Answer

d()/d(x)8/(3*x2)=−16/(3*x3)

Want more problems? Check here!