Find the Derivative - d/d@VAR f(x)=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 power rule to each term individually, which states that d(xn)/d(x)=n*x(n−1)

(d(4)*x(−2))/d(x)=4*(−2)*x(−3)

(d(−)*10*x3)/d(x)=−10*(3)*x2

3. Simplify the coefficients and exponents.

4*(−2)*x(−3)=−8*x(−3)

−10*(3)*x2=−30*x2

4. Convert the negative exponent back into a fraction for the final form.

−8*x(−3)=−8/(x3)

Final Answer

d()/d(x)*(4/(x2)−10*x3)=−8/(x3)−30*x2

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