Chapter 2: Q. 72 (page 223)
Use implicit differentiation and the fact that is the inverse of to prove that
Short Answer
The given differentiation has been proved.
Chapter 2: Q. 72 (page 223)
Use implicit differentiation and the fact that is the inverse of to prove that
The given differentiation has been proved.
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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 graphed in Exercises 65-68, determine the values of at which fails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.
Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra
Use (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23–38.
28.
Suppose f is a polynomial of degree n and let k be some integer with . Prove that if f(x) is of the form
Then where is the k-th derivative of
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