Find the Derivative - d/d@VAR f(x)=0.002x^3+8+7626/x

Problem

d()/d(x)*(0.002*x3+8+7626/x)

Solution

1. Rewrite the expression using power notation to make differentiation easier, specifically changing the fraction to a negative exponent.

ƒ(x)=0.002*x3+8+7626*x(−1)

2. Apply the power rule to the first term, 0.002*x3 by multiplying the coefficient by the exponent and subtracting one from the exponent.

(d(0.002)*x3)/d(x)=0.006*x2

3. Apply the constant rule to the second term, 8 noting that the derivative of any constant is zero.

d(8)/d(x)=0

4. Apply the power rule to the third term, 7626*x(−1) by multiplying the coefficient by −1 and subtracting one from the exponent.

(d(7626)*x(−1))/d(x)=−7626*x(−2)

5. Combine the results and rewrite the negative exponent as a fraction to obtain the final derivative.

ƒ(x)′=0.006*x2−7626/(x2)

Final Answer

d()/d(x)*(0.002*x3+8+7626/x)=0.006*x2−7626/(x2)

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