Find the Derivative - d/dx -1/3(x^-3-x^6)

Problem

d()/d(x)*(−1/3*(x(−3)−x6))

Solution

1. Distribute the constant −1/3 into the parentheses to simplify the expression before differentiating.

−1/3*(x(−3)−x6)=−1/3*x(−3)+1/3*x6

2. Apply the sum rule for derivatives, which allows for the differentiation of each term individually.

d()/d(x)*(−1/3*x(−3)+1/3*x6)=d()/d(x)*(−1/3*x(−3))+d()/d(x)*(1/3*x6)

3. Apply the power rule d(xn)/d(x)=n*x(n−1) to each term.

d()/d(x)*(−1/3*x(−3))=−1/3*(−3)*x(−4)=x(−4)

d()/d(x)*(1/3*x6)=1/3*(6)*x5=2*x5

4. Combine the results of the derivatives.

x(−4)+2*x5

Final Answer

d()/d(x)*(−1/3*(x(−3)−x6))=x(−4)+2*x5

Want more problems? Check here!