Homework SourseThe below question was answered by long hand and was very ha
The below question was answered by long hand and was very hard to read. Please re-submitt - Thanks
Calculate the derivative of 3x^-4 using both the definition of the derivative, and the Product rule. What is the derivative and what are the differences in these two procedures? If you think one might be better or not, explain why it is. In general, which is preferable, using the definition or using the derivative rules? Why?
Calculate the derivative of 3x^-4 using both the definition of the derivative, and the Product rule. What is the derivative and what are the differences in these two procedures? If you think one might be better or not, explain why it is. In general, which is preferable, using the definition or using the derivative rules? Why?
Solution
using definition of derivative d(x^n)/dx=nx^(n-1) so it gives -12x^(-5) using product rule:d(fg)/dx=fdg/dx+gdf/dx let3x^(-4)=3x^(-2)*x^(-2) so by the rule derivative is 3[x^(-2)*(-2x^-3)+x^(-2)*(-2x^-3)] =-12x^(-5)
