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1. Find the derivatives of the following functions using derivative rules from Sections 4.3/4.4. Show your work (indicate which rules were used). You do not need to simplify your answers. 2 (a) f(x) = = (b) g(x) = (3x +2)(6x + 5)4 (t +3)(VE + 1) (c) h(t) = t+ 2

1. Find the derivatives of the following functions using derivative rules from Sections 4.3/4.4. Show your work (indicate which rules were used). You do not need to simplify your answers. 2 (a) f(x) = = (b) g(x) = (3x +2)(6x + 5)4 (t +3)(VE + 1) (c) h(t) = t+ 2

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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Thank you kindly! (The derivative rules from section 4.3 & 4.4 are in the second image) :)
Derivative of a Constant Function d Let c be a constant, then -(c) = 0. dx The Power Rule If n is a real number, then -(x") = nx"-1. The Constant Multiple Rule If c is a constant and f is a differentiable function, then d d -[cf (x)] = cf(x). dx The Sum and Difference Rules If f and g are both differentiable functions, then * (f(x) + g(x)) = and d - (f(x) – g(x)) = xp The Product Rule If f and g are both differentiable functions, then = f(x The Quotient Rule If f and g are both differentiable functions, then g(x) [f(x)] – f(x) [g(x)] [g(x)]² d [f(x) dx The Chain Rule If g is differentiable at x and f is differentiable at g(x), then the composite function h(x) = (f o g)(x) = f(g(x)) is differentiable at x and h'(x) is given by: h'(x) = f'(g(x)) · gʻ(x).
Transcribed Image Text:Derivative of a Constant Function d Let c be a constant, then -(c) = 0. dx The Power Rule If n is a real number, then -(x") = nx"-1. The Constant Multiple Rule If c is a constant and f is a differentiable function, then d d -[cf (x)] = cf(x). dx The Sum and Difference Rules If f and g are both differentiable functions, then * (f(x) + g(x)) = and d - (f(x) – g(x)) = xp The Product Rule If f and g are both differentiable functions, then = f(x The Quotient Rule If f and g are both differentiable functions, then g(x) [f(x)] – f(x) [g(x)] [g(x)]² d [f(x) dx The Chain Rule If g is differentiable at x and f is differentiable at g(x), then the composite function h(x) = (f o g)(x) = f(g(x)) is differentiable at x and h'(x) is given by: h'(x) = f'(g(x)) · gʻ(x).
1. Find the derivatives of the following functions using derivative rules from Sections 4.3/4.4. Show your work (indicate which rules were used). You do not need to simplify your answers. 2 (a) f(x) = 3 (b) g(x) = (3x + 2)(6x + 5)4 (t+ 3)(Vt + 1) (c) h(t) = t +2
Transcribed Image Text:1. Find the derivatives of the following functions using derivative rules from Sections 4.3/4.4. Show your work (indicate which rules were used). You do not need to simplify your answers. 2 (a) f(x) = 3 (b) g(x) = (3x + 2)(6x + 5)4 (t+ 3)(Vt + 1) (c) h(t) = t +2
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