Find the Derivative - d/dx 12-192/(x^2)

Problem

d()/d(x)*(12−192/(x2))

Solution

1. Rewrite the expression using negative exponents to make differentiation easier.

12−192*x(−2)

2. Apply the sum rule for derivatives, which allows for the differentiation of each term separately.

d(12)/d(x)−(d(192)*x(−2))/d(x)

3. Differentiate the constant term, noting that the derivative of any constant is zero.

d(12)/d(x)=0

4. Apply the power rule to the second term by multiplying the coefficient by the exponent and subtracting one from the exponent.

−192⋅(−2)*x(−2−1)

5. Simplify the resulting expression by performing the multiplication and converting the negative exponent back into a fraction.

384*x(−3)

384/(x3)

Final Answer

d()/d(x)*(12−192/(x2))=384/(x3)

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