Find the Derivative - d/dx 9/x-2/(x^3)+1/(x^4)

Problem

d()/d(x)*(9/x−2/(x3)+1/(x4))

Solution

1. Rewrite the expression using negative exponents to prepare for the power rule.

9/x−2/(x3)+1/(x4)=9*x(−1)−2*x(−3)+x(−4)

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

(d(9)*x(−1))/d(x)=9*(−1)*x(−2)=−9*x(−2)

(d(−)*2*x(−3))/d(x)=−2*(−3)*x(−4)=6*x(−4)

d(x(−4))/d(x)=−4*x(−5)

3. Combine the resulting terms into a single expression.

−9*x(−2)+6*x(−4)−4*x(−5)

4. Simplify the expression by converting the negative exponents back into fraction form.

−9/(x2)+6/(x4)−4/(x5)

Final Answer

d()/d(x)*(9/x−2/(x3)+1/(x4))=−9/(x2)+6/(x4)−4/(x5)

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