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2) Use the Chain Rule to express the second derivative of ƒog in terms of the first and second derivatives of f and g.

2) Use the Chain Rule to express the second derivative of ƒog in terms of the first and second derivatives of f and g.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1) Find the hundredth derivative of p (x) = (x + x³ + x")1º (1+ x²)!' (x³ + x³ + x"). Justify your answer. 2\11 2) Use the Chain Rule to express the second derivative of fogin terms of the first and second derivatives of f and g. 3) Show that for any constants M, k, and a, the function ´k(t – — а) y(t) M1+tanh satisfies the logistic equation: = kl 1 Note: The function tanh is the hyperbolic tangent function 2: tanh x = et - e 2x 1 et +e-x 2x +1 4) The lemniscate curve (x2 + y² )² = 4(x² – y²) was discovered by Jacob Bernoulli in 1694, who noted that it is "shaped like a figure 8, or a knot, or the bow of a ribbon." Find the coordinates of the four points at which the tangent line is horizontal.
Transcribed Image Text:1) Find the hundredth derivative of p (x) = (x + x³ + x")1º (1+ x²)!' (x³ + x³ + x"). Justify your answer. 2\11 2) Use the Chain Rule to express the second derivative of fogin terms of the first and second derivatives of f and g. 3) Show that for any constants M, k, and a, the function ´k(t – — а) y(t) M1+tanh satisfies the logistic equation: = kl 1 Note: The function tanh is the hyperbolic tangent function 2: tanh x = et - e 2x 1 et +e-x 2x +1 4) The lemniscate curve (x2 + y² )² = 4(x² – y²) was discovered by Jacob Bernoulli in 1694, who noted that it is "shaped like a figure 8, or a knot, or the bow of a ribbon." Find the coordinates of the four points at which the tangent line is horizontal.
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