Find the Derivative - d/dx 1/(5x^2)

Problem

d()/d(x)1/(5*x2)

Solution

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

1/(5*x2)=1/5*x(−2)

2. Apply the constant multiple rule, which allows the constant factor to be moved outside the derivative.

d()/d(x)1/5*x(−2)=1/5d(x(−2))/d(x)

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

1/5*(−2*x(−2−1))=−2/5*x(−3)

4. Simplify the expression by moving the variable back to the denominator with a positive exponent.

−2/5*x(−3)=−2/(5*x3)

Final Answer

d()/d(x)1/(5*x2)=−2/(5*x3)

Want more problems? Check here!