CH 2 Handout review_page_1
Math 2413 Instructor: Adnan Said Chapter 2: Sections 2.1, 2.2, 2.3, 2.4, 2.5, and 2.6 2.1 The Derivative and the Tangent Line Problem…
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The Chain Rule versions of the derivatives of the six trigonometric functions are: The Sine and Cosine Functions Rules 4 gin uj = (cos u)u'…
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2.5 Implicit differentiation Implicit and Explicit Functions A function that is implied by an equation is said to be written in implicit…
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33) 4x2y - m cos y=5n Solution: u=4x2>u'=8xk ; v=y >v=y (8x)y + y (4x2) — 1 (-sin y) y' = 0 — 8xy + 4y'x2 +7 siny y =0 > dy'x2+nsiny y'…
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2.6 Related Rates Implicit differentiation is useful in finding the rates of change of two or more related variables that are changing with…
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37) Air is being pumped into a spherical balloon at a rate of 4.5 cubic feet per minute. Find the rate of change of the radius when the…
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Find the equation of the tangent line to the graph of f(x) at the point where x = 1. 2) £(x) = x2 - 4x. 2) From problem #1, f (x) = 2x-4.…
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Existence of the Derivative A function is differentiable at x if its derivative exists at x. A function is not differentiable in three…
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2.2. Basic Differentiation Rules Basic Differentiation Rules The Sum or Difference Rules: u(x) + v(x) | = u'(x) + v'(x) x The Constant…
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9) £2) if £69 = 2X72 4x2 9) x f(x) = (2x7 - 4x2)x - 4 = 2x3 - 4x -2 f '(x) = 2(3)x2 - 4(-2)x -3 = 6x2 + 8x -3 £ (2) = 6(2)2 + 8(2)-3 = 6(4)…
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2.3 Product and Quotient Rules and Higher-Order Derivatives The Product Rule: Subs - v(x)] = u(x) « vod) + v'(x) + u(x) x Find the…
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I y= x _ xl/2 2x2-4 2x2-4 u(x) = x1/2 > u'(x) = oe? > v(x) = 2x2 -4 > v'(x) = 4x 1-1/2 (22 ~ 4) - 4x(x1/2) §'0) <2 _ x3/2— 2x -1/2 ~ 43/2…
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Higher - Order Derivatives f (x) is the second derivative of the function also written as dey. dx2 f (x) is the third derivative of the…
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2.4 The Chain Rule The Chain Rule If y is a function of u, and u is a function of x, then dy _ dy , du dx du dx A special case of the chain…