Answer : Option - ( D )
Option - ( D ) Represents the product rule for Derivative
7. Which of these represents the product rule for derivatives? A. For f(x) = (C *x"), f' (x) = C ...
Use the Chain Rule and the fact that d (r)-L,o find the derivative of (b) Rewrite f(x) as a piecewise function not involving the absolute value function. (c) Find the first and second derivatives of f(x),using your piecewise function. (d) Would you want to find" without the function's piecewise representation? 2. A square and a triangle are to be cut from a piece of fabric 1 metre square, as shown Find the length which minimises the removed area ar Use...
1. Derivatives practice: a. Find the marginal product of labor when F(x)-4KL (Take the derivative with respect to L b. Find the marginal product of capital when F(x)-4KL (Take the derivative with respect to Find the marginal product of labor when F(x) = 61K3 (Take the derivative with respect to L). c. d. Find the marginal product of labor when F(x) 61/2 K1/ (Take the derivative with e. Find the marginal product of labor when F(x) = 11/4K3/4 (Take the...
W MATHEMATICAL ASSOCIATION OF AMERICA webwork i mat1475-520-sirelson-d601 / derivatives_-_product_rule / 2 Derivatives - Product Rule: Problem 2 Previous Problem Problem List Next Problem (1 point) Library/Michigan/Chap3Sec3/Q31.pg Use the figure below to estimate the indicated derivatives, or state that they do not exist. If a derivative does not exist, enter dne in the answer blank. The graph of f(x) is black and has a sharp comer at 2. The graph of g() is blue. Let h() - f(x) (). Find...
Let f be a function having derivatives of all orders for all real numbers. Selected values of f and its first four derivatives are shown in the table above. (a) Write the second-degree Taylor polynomial for f about x = 0 and use it to approximate f(0.2). (b) Let g be a function such that g(x) =f(x3). Write the fifth-degree Taylor polynomial for g', the derivative of g, about x = 0. (c) Write the third-degree Taylor polynomial for f about x =...
4. For f(x) = e-* and h = 0.10 where, C = 1.** a) Use centered approximations to estimate the first and second derivatives of f(x) at x = 2. Use the east accurate formulas available. (10 pts) b) Using the most acurate forward and backward difference formulas, estimate the first derivative of f(x) at x 2. (10 pts) Forward Difference First Derivative 7.) - SD Error OM or) = -1.) + 40..) - 3 ) 2h Second Derivative 'w...
(Product Rule) Use the Product Rule to find the derivative of the function. f(x) = (4x+5)(x2 -8) O a. 2x + 4 Ob. 12x² + 10x - 32 O c. 8x O d. 8x2 – 40
1) Let f:R-->R be defined by f(x) = |x+2|. Prove or Disprove: f is differentiable at -2 f is differentiable at 1 2) Prove the product rule. Hint: Use f(x)g(x)− f(c)g(c) = f(x)g(x)−g(c))+f(x)− f(c))g(c). 3) Prove the quotient rule. Hint: You can do this directly, but it may be easier to find the derivative of 1/x and then use the chain rule and the product rule. 4) For n∈Z, prove that xn is differentiable and find the derivative, unless, of course, n...
21. Find the derivative of each of the following functions by applying the product rule a. f(x) = (x2 + 1][2x2 + 3x + 4) b. f(x) = x2 cos x c. f(x) = e* sin x 22. Find Find the derivative of each of the following functions by applying the quotient rule a. f(x) = 22+1 f(x) = (2x + 1] / [x - 3] b. f(x) = x+2x+1 3x + 1 c. f(x) = sing 23. Find the...
(8) Let E C R" and G C R" be open. Suppose that f E G and g G R', so that h = go f : E → R. Prove that if f is differentiable at a point x E E, and if g is differentiable at f (x) E G, then the partial derivatives Dihj(x) exist, for all and j - ...., and 7m に! (The subscripts hi. g. fk denote the coordinates of the functions h, g....
Verify the product rule for Formal Power Series. Very specifically: Let f(x) be the generating function for a sequence san) and g(x) be the generating function for a sequence sbn1. Using the definitions of multiplication and differentiation of FPS, write down a formula for the derivative of [f(x)g(x)]. Then write down a formula for f(x)g(x) + f(x)g'(x), where f(x) denotes the derivative of f(x). Then show that the two formulas describe the same formal power series. (i.e. both series have...