Find the Derivative - d/d@VAR h(x)=8/x-2/(x^3)+1/(x^4)

Problem

d()/d(x)*(8/x−2/(x3)+1/(x4))

Solution

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

h(x)=8*x(−1)−2*x(−3)+x(−4)

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

d(h(x))/d(x)=8*(−1)*x(−2)−2*(−3)*x(−4)+(−4)*x(−5)

3. Simplify the coefficients and the signs for each term.

d(h(x))/d(x)=−8*x(−2)+6*x(−4)−4*x(−5)

4. Convert the expression back into fraction form by moving the variables with negative exponents to the denominators.

d(h(x))/d(x)=−8/(x2)+6/(x4)−4/(x5)

Final Answer

d()/d(x)*(8/x−2/(x3)+1/(x4))=−8/(x2)+6/(x4)−4/(x5)

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