Find the Derivative - d/dx 9/(8x^2)

Problem

d()/d(x)9/(8*x2)

Solution

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

9/(8*x2)=9/8*x(−2)

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

d()/d(x)9/8*x(−2)=9/8d(x(−2))/d(x)

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

9/8d(x(−2))/d(x)=9/8*(−2*x(−3))

4. Simplify the resulting expression by multiplying the constants and rewriting the negative exponent as a fraction.

9/8*(−2*x(−3))=−18/8*x(−3)

5. Reduce the fraction and move the variable back to the denominator.

−18/8*x(−3)=−9/(4*x3)

Final Answer

d()/d(x)9/(8*x2)=−9/(4*x3)

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