Find the Derivative - d/dx 7/(6x^2)

Problem

d()/d(x)7/(6*x2)

Solution

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

7/(6*x2)=7/6*x(−2)

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

d()/d(x)7/6*x(−2)=7/6⋅(−2)*x(−2−1)

3. Simplify the coefficient by multiplying 7/6 and −2

7/6⋅(−2)=−14/6=−7/3

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

−7/3*x(−3)=−7/(3*x3)

Final Answer

d()/d(x)7/(6*x2)=−7/(3*x3)

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