Derivative ln f x
[DOC File]Calculus I
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6.) Suppose f is a function. Suppose that f'(2) = 0. Suppose further that if x < 2, f'(x) > 0 and if x > 2, f'(x) < 0. What does this mean? Why? 7.) Explain the origins of the formula for the definition of the derivative. Use complete sentences and proper grammar. Use figures …
[DOC File]Derivative of ax and ex
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5. f(x) = (ln 4) 4x 6. f(x) = (2x. 7. f(x) = e2x 8. f(x) = 9. f(x)= 10. f(t)= (e –t + et )3 . 11. f(x)=x2ex –2xex + 2ex 12. f(x)= 13. Find the second derivative of the function: f(x) = ( 3+2x)e-3x. A52. Title: Derivative of ax and ex Author: Mary Selcer Last modified by: Windows User Created Date: 1/10/2014 7:05:00 PM Company: Compaq Other ...
[DOC File]AP Calculus Free-Response Questions
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442. Let f be the function defined for x > 0, with f(e) = 2 and f′, the first derivative of f, given by f′(x) = x2 ln x. a. Write an equation for the line tangent to the graph of f at the point (e, 2). b. Is the graph of f concave up or concave down on the interval 1 < x < 3? Give a reason for your answer. c. Use antidifferentiation to find ...
[DOC File]Topic 4: Differentiation
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If x = f(y) then . The derivative of the inverse of the function x = f(y), is the inverse of the derivative of the function (i) x = 3y2 then . so (ii) y = 4x3 then . so Differentiating functions using Rules 1 ( 8, See Section 4 of course manual, questions 3, 4 and 10 Applications of the Basic Rules . Calculating Marginal Functions. Example 1
[DOCX File]The Derivative of the Natural Logarithmic Function
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Theorem Derivative of the Natural logarithmic function or In particular, Proof: Ex 5 Find the derivative of . y wrt x, t, or θ , as appropriate. y= ln 10 x . y= ln kx , k constant . y= ln ( t 3/2 ) y= ln x 3 . y= t 2 ln 3t . y= ln 1+ ln ln x . y= ln sin θ cos θ 1+2 ln θ (Recall: ln xy =lnx+ln y and ln x y =lnx-lny & Sin 2x=2Sinx Cosx )
[DOC File]Derivatives - UH
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Take the derivative of f(x) and set it equal to zero: Note that there’s a common factor of twelve, divide it out: Use the Rational Root theorem and synthetic division to find that the factors of the derivative are. 12(x + 3)(x ( 2)(x + 1) So the turn around points are at x = (3, x = 2, and x = (1.
[DOC File]AP Calculus Assignments: Derivative Techniques
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c. Hypothesize a general rule about the derivative of a continuous function f and the invertibilty of f. d. Use calculus to prove that the function f(x) = x3 + 4x – 5 has an inverse function.
[DOCX File]November 12, 1997
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Let’s try to prove the derivative of the function f x =tan x using trigonometric identities: f x = tan x = sin x cos x . Using the quotient rule determine the derivative of . f x .Let’s try to prove the derivative of the function . g x = sec x using trigonometric identities: g x = sec x = 1 cos x …
[DOC File]The Derivative of the General Exponent Function y = bx
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If f(x) = bg(x), then f’(x) = bx · ln b · g’(x) e.g. f(x) = 35x, then f’(x) = 35x · ln3 · 5. Notice: This works for f(x) = ex, f’(x) = ex · ln e = f’(x) = ex · (1) = e x since ln e = 1. 1. Take the derivative of the following functions. a) f(x) = 2 3x b) f(x) = 2.7x + x4 c) f(x) = 6 6t – 2t^2. d) f(x) = x4 · 5 x e) h(t) = 2 t ...
[DOC File]AP Calculus Free-Response Questions
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3. Given f(x) = + ln x, defined only on the closed interval ≤ x ≤ e, a. Showing your reasoning, determine the value of x at which f has its (i) absolute maximum, (ii) absolute minimum. b. For what values of x is the curve concave up? c. On the coordinate axes provided, sketch the graph of f over the interval ≤ x …
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