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Suppose f is a one-to-one, differentiable function and its inverse function f-¹ is also differentiable. One can show, using implicit differentiation (do it!), that (f¹)'(x) = Find (f¹)'(4) if f(2) = 4 and ƒ'(2) = 3/7. (ƒ-¹)'(4) = 1 ƒ'(ƒ−¹(x))

Suppose f is a one-to-one, differentiable function and its inverse function f-¹ is also differentiable. One can show, using implicit differentiation (do it!), that (f¹)'(x) = Find (f¹)'(4) if f(2) = 4 and ƒ'(2) = 3/7. (ƒ-¹)'(4) = 1 ƒ'(ƒ−¹(x))

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.CR: Chapter 9 Review
Problem 54CR
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Suppose f is a one-to-one, differentiable function and its inverse function f-¹ is also differentiable. One can show, using implicit differentiation (do it!), that (f¹)'(x) = Find (f¹)'(4) if f(2) = 4 and ƒ'(2) = 3/7. (ƒ-¹)'(4) = 1 ƒ'(ƒ−¹(x))
Transcribed Image Text:Suppose f is a one-to-one, differentiable function and its inverse function f-¹ is also differentiable. One can show, using implicit differentiation (do it!), that (f¹)'(x) = Find (f¹)'(4) if f(2) = 4 and ƒ'(2) = 3/7. (ƒ-¹)'(4) = 1 ƒ'(ƒ−¹(x))
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