Question G. [5 MARKS] Find the derivative of y, where y is given implicitly as a...
(a) Find the following derivative: d In (5.y dz dB (6 marks) (b) Consider the following bivariate function: g(x,y)exp 8B In (4x2y2)] Find the elasticity of g with respect to x (6 marks) (a) Find the following derivative: d In (5.y dz dB (6 marks) (b) Consider the following bivariate function: g(x,y)exp 8B In (4x2y2)] Find the elasticity of g with respect to x (6 marks)
QUESTION 4 Find the derivative of the function. OOOO QUESTION 5 Find the derivative. OOO y = 4x2 + 7x + 3e * 8x + 3e* 8x + 7 + ex 8x + 7 + 3e* 4x + 3e* + + QUESTION 6 Find the derivative. y = 14 - 7x2 14 - 14x 0-14 14 - 7x O-144
Find the derivative of the function. y sin-1(5x+ 1) Part 1 of 3 The function y - sin-1(5x + 1) is a composition, and so we must use the Chain Rule, given below, to find the derivative dx[f(g(x))) = f '(g(x))g'(x) For the given function sin 1(5x+ 1), the "inside" function is Sx + and the foutside" function is arcsin (a) Part 2 of 3 Recall that the derivative of y sin-1(x) is 1-(5x - 1)2 Find the derivative of...
by differentiating implicitly. Express your answers in terms 5. (2 marks) Find of x and y. dx a) 3ay – y2 = 5 b) 2y = x2 – 3x +2y 6. (2 marks) The position of an object "S" (in meters) at time tis given by the function: s(t) = (31)cos(t)+41. a) What is the velocity when t = 24 seconds? Indicate the correct units and round your answer to one decimal place. b) What is the acceleration when 1...
please do #7 the derivative of the function y - tan-(x-v1+x? ). Problem 5. Find the derivative of the function y = sin(2x+1). Problem 6. Find the derivative of the function h(x) = sinh(x?). Problem 7. Find the limits. Use L'Hospital's Rule where appropriate. I (a) lim x’e-* (b) lim (sin x In x) x0+
2. (each 1 mark) Find the derivative of the following functions: 9x + 7 (a) y = 92 - 1 (b)r = (02 9016 /09 - 9 ( 9 ) (c) y=rºcot x + 9x2 cos x – 14x sin x 9t sint (d) s = cost + +9 (e) h(x) = cº sin (vą) + 240 sec (1) ) 10 (f) f(0) = (_sin 98 (1+cos 90 ) (g) g(x) = (1 + csc(+10) + In (922 – 8)...
Differentiate implicitly to find the first partial derivatives of z. x In(y) + y2z + ? = 49 az Ox = az ay = 10. (-/1 Points] DETAILS ALC11 13.6.009. Find the directional derivative of the function at P in the direction of v. g(x, y) = x2 + y2, P(7, 24), v = 5i - 123
Chapter 3, Review Exercises, Question 036 Find the derivative of the given function. g(x) = arctan(8x2 + 6) 9 (x) = 2 Edit Luapter 3, Review Exercises, Question 043 Find the derivative of the given function. y = 3* + 2 y 12 Edit Click if you
Find the derivative of the trigonometric function. y = sin((rex)5) y'(x) = ||
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 +...