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5. Recall that y = sec-¹x (with domain x ≥ 1) means sec y=x and 0 ≤y2 or T ≤ y ≤ 37/2. Use implicit differentiation to derive the formula d dx - (sec-¹x) = 1 x√x² .

5. Recall that y = sec-¹x (with domain x ≥ 1) means sec y=x and 0 ≤y2 or T ≤ y ≤ 37/2. Use implicit differentiation to derive the formula d dx - (sec-¹x) = 1 x√x² .

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.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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5. Recall that y = sec-¹x (with domain |x|≥ 1) means sec y = x and 0 ≤ y ≤ π/2 or π ≤ y ≤ 3π/2. Use implicit differentiation to derive the formula (sec-¹x) d dx = 1 x√x² 1 1 - 6. The hyperbolic cosine function cosh x (pronounced 'kosh') is used to describe a catenary, the shape of a hanging cable. The derivative is (cosh x)' sinh x, the hyperbolic sine function (pronounced 'sinch'). Note that there is no negative on the derivative as there is with the 'regular' cosine derivative. = The following identity holds for these functions: cosh² y-sinh² y = 1. For the inverse function we have y = cosh¹ x means cosh y = x. Use these facts and implicit differentiation to derive
Transcribed Image Text:5. Recall that y = sec-¹x (with domain |x|≥ 1) means sec y = x and 0 ≤ y ≤ π/2 or π ≤ y ≤ 3π/2. Use implicit differentiation to derive the formula (sec-¹x) d dx = 1 x√x² 1 1 - 6. The hyperbolic cosine function cosh x (pronounced 'kosh') is used to describe a catenary, the shape of a hanging cable. The derivative is (cosh x)' sinh x, the hyperbolic sine function (pronounced 'sinch'). Note that there is no negative on the derivative as there is with the 'regular' cosine derivative. = The following identity holds for these functions: cosh² y-sinh² y = 1. For the inverse function we have y = cosh¹ x means cosh y = x. Use these facts and implicit differentiation to derive
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