Find the Derivative - d/dx 1/(8x^2)

Problem

d()/d(x)1/(8*x2)

Solution

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

1/(8*x2)=1/8*x(−2)

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

d()/d(x)1/8*x(−2)=1/8⋅(−2)*x(−2−1)

3. Simplify the coefficient by multiplying the fraction and the integer.

1/8⋅(−2)=−2/8=−1/4

4. Simplify the exponent and rewrite the expression with a positive exponent.

−1/4*x(−3)=−1/(4*x3)

Final Answer

d()/d(x)1/(8*x2)=−1/(4*x3)

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