Find the Derivative - d/dx 4/(x^2)-10x^3

Problem

d()/d(x)*(4/(x2)−10*x3)

Solution

1. Rewrite the first term using a negative exponent to prepare for the power rule.

4/(x2)=4*x(−2)

2. Apply the sum rule for derivatives to differentiate each term separately.

d()/d(x)*(4*x(−2)−10*x3)=(d(4)*x(−2))/d(x)−(d(10)*x3)/d(x)

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

(d(4)*x(−2))/d(x)=4*(−2)*x(−3)=−8*x(−3)

(d(10)*x3)/d(x)=10*(3)*x2=30*x2

4. Combine the results and rewrite the negative exponent as a fraction.

−8*x(−3)−30*x2=−8/(x3)−30*x2

Final Answer

d()/d(x)*(4/(x2)−10*x3)=−8/(x3)−30*x2

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