Chapter 2: Q. 85 (page 199)
Use thedefinition of the derivative to prove the power rule holds for positive integers powers
Short Answer
We prove the power rule holds for positive integers powers using the definition of derivative
Chapter 2: Q. 85 (page 199)
Use thedefinition of the derivative to prove the power rule holds for positive integers powers
We prove the power rule holds for positive integers powers using the definition of derivative
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Get started for freeFind the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
For each function f and value in Exercises 35–44, use a sequence of approximations to estimate . Illustrate your work with an appropriate sequence of graphs of secant lines.
In Exercises 69–80, determine whether or not f is continuous and/or differentiable at the given value of x. If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.
Prove, in two ways, that the power rule holds for negative integer powers
a) by using the definition of the derivative
b) by using thedefinition of the derivative
Find the derivative of the absolute value function and piecewise defined function
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