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Finding and Evaluating a Derivative In
Exercises 17–24, find f x and f c.
23. f (x) = ex sin x, c = 0
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- Temperature The graph shows the temperature in degrees Celsius as a function of the altitude h in feet when an inversion layer is over Southern California. See Exercise 43 in the previous section. Estimate and interpret the derivatives of T(h) at the marked points.Module 3: Participation Activity #3 Find the derivative of f(x)=2csc(x). Enclose arguments of functions in parentheses. For example, sin(2x). f′(x)=et Consider the function f(x) = Compute the derivative of this function. 5 + et
- Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the derivative does not exist at c, enter UNDEFINED.) h(x) = |x + 1|, c = -1 h'(-1) = Need Help? Read It Watch It Talk to a Tutor3x2 + 2x Determine the derivative of the function f(x) cot xUse the alternative form of the derivative to find the derivative at x = c (if it exists). (If the derivative does not exist at c, enter UNDEFINED.) f(x) = x + 2x² + 3, c = -2 f'(-2) = Need Help? Read It Watch It Master It
- Using the alternative form of the derivative. Use the alternative form of the derivative to find the derivative at x=c if it exists.Finding the derivative and finding the equation of the tangent line Finding f'(x) from the Definition of Derivative The four steps used to find the derivative f'(x) for a function y = f(x) are summarized here. Part -a. Part-b 1. Find and simplify f(x + h). 2. Find and simplify ƒ(x + h) — f(x). 3. Find and simplify the quotient ƒ(x + h) − f(x) h 4. Find the limit as h approaches 0; f'(x) = lim f(x)=2x² Find the f'(x) using the definition f'(x) = Lim₁ 0 f(x+h)-f(x) h f(x + h) − f(x) After find in the f'(x) in Part-a a. find f'(2) b. find f(2) c. Find the equation of the tangent line at x=2 if this limit exists. 1 (Use the steps given above and the lesson posted)Using the definition, calculate the derivatives of the functions inExercise Then find the values of the derivatives as specified.2. F(x) = (x - 1)^2 + 1; F′(-1), F′(0), F′(2)
- Direction: Illustrate the Chain Rule of differentiation by determining the derivatives of the outer and inner functions of the given functions and finding the differentiation using the Chain Rule to complete the table. Differentiate Derivative of outer Function Derivative of inner function Differentiation d. f(x)= (5x-3)2 e. y=cos (5x)Find the derivative of the function. f(x) = sin-¹ (6x) f'(x) = -6 cot (6x) csc (6x) CSC Need Help? Read It × Master It Submit Assignment Save Assignment ProgressDirection: Illustrate the Chain Rule of differentiation by determining the derivatives of the outer and inner functions of the given functions and finding the differentiation using the Chain Rule to complete the table. Differentiate Derivative of outer Function Derivative of inner function Differentiation a. y= sin (2x) b. f(x)= square root of (x2=1) c. y= (5x2-3x+1)2 d. f(x)= (5x-3)2 e. y=cos (5x) f. f(x)=e(5z^2+7z-13)