Question 2 of 14 (1 point) Differentiate the given function. The derivative of the function is...
Use the definition of the derivative to differentiate the following function: f(x) 1 x + 2
QUESTION 9 Apply the techniques of logarithmic differentiation to find the derivative of the given function f(x). [Hint: first take the logarithm of both sides and simplify using properties of logarithms. Then differentiate implicitly.) F) - ** (3x+1) {f(x) = {{x^2 (3x + 1)^3} /(sqrt(x^2 + 4))] } TTTT Paragi Arial 3 (12p *DOQ E T' T. . 15 25 Path: P QUESTION 10 Find the derivative of the following expression involving inverse trigonometric functions. g(x) = arctan x +...
Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xyz, (4,2, 8), v = (-1, -2, 2) Duf(4, 2, 8) = -4 X
Please answer all 3.
Complete the table to find the derivative of the function. Original Function Rewrite Differentiate Simplify 5 y = - fax2 80x Need Help? Read It Talk to a Tutor [-/1 Points] DETAILS LARCALCET7 3.2.034. MY Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. Function y = 9x4 - 10 Point (1, -1) y'(1) = Need Help? Read It Talk...
(1 point) The given graph of the derivative f' of a function f is shown. Assuming the graphs continue in the same way as x goes to infinity and negative infinity, answer the following questions. 1. On what intervals is f increasing? Answer (in interval notation): [-3.2,-1]U[2.5,Inf) 2. On what intervals is f decreasing? Answer (in interval notation): (-Inf,-3.2]U[-1,2.5] Note: You can click on the graph to enlarge the image.
6. For a given function f(x, y), is noted that at the point P(1,1) the directional derivative in the direction towards (0,0) is 1, while the directional derivative towards (1.2) is -1. Find andf at
6. For a given function f(x, y), is noted that at the point P(1,1) the directional derivative in the direction towards (0,0) is 1, while the directional derivative towards (1.2) is -1. Find andf at
Exercise 2 Suppose un(x) = x(1/2), the positive square-root function. For this function, the derivative function, u(x), is the function (1/2)1). In the same graph, sketch x(1/2) and (1/2)i) For this case, express the slope of the indifference through the point (Cu1, Gna) in terms of tuo ratios (T1/T2) and (c2/n1). Interpret the way the slope of the indifference through the point (cn1, Cn2) depends on those two ratios.
1) Find the directional derivative of the function at the given point and in the direction of the vector u as shown when f(x,y)= sen(2x+3y); (-6,4); u=(1/2)(sqrt(3)),-1) POSSIBLE ANSWERS A) sqrt(3)-(3/2) B) (3/2)+sqrt(3) C) (3/2)-sqrt(3) D) -(3/2)-sqrt(3) 2) Find the direction in which the function is growing or decreasing more rapidly at the point shown: f(x,y)=x(e^y)-lnx; (4,0) POSSIBLE ANSWERS: A) u=(3/(sqrt(265)) , 16/(sqrt(265))) B)u=(3/(sqrt(265)) , -16/(sqrt(265))) C)u=(16/(sqrt(265)) , 3/(sqrt(265))) D)u=(-3/(sqrt(265)) , 16/(sqrt(265)))
15 Problem 12 (5 point) Assume that f(x) is a function whose nth derivative is given by (-1)"2 (2n)!(x + 1)+1 Given the Taylor series of f(x) centered at a = 2 using sigma notation and find the radius of convergence