(a) Find the following derivative: d In (5.y dz dB (6 marks) (b) Consider the following bivariate function: g(x,y)exp 8...
Consider the following. 7 g(t) = 846 Find the first derivative of the function. g'(t) = Find the second derivative of the function. g"(t) = X Use the General Power Rule to find the derivative of the function. 1 y = 3 (8 - x3,8 y' = Find the derivative of the function. 3 8x 5 Y= 뉴 4-X y =
Question G. [5 MARKS] Find the derivative of y, where y is given implicitly as a function of x by: ytan + y sin cIn y = 14.
6) Use MATLAB and Newton-Raphson method to find the roots of the function, f(x) = x-exp (0.5x) and define the function as well as its derivative like so, fa@(x)x^2-exp(.5%), f primea@(x) 2*x-.5*x"exp(.5%) For each iteration, keep the x values and use 3 initial values between -10 & 10 to find more than one root. Plot each function for x with respect to the iteration #.
Find the derivative of the function. g(x) = 800(3 - e-0.1x) Find the derivative of the function. y = :ets Find the derivative of the function. y = 4e(x2 + 6)3 Find the derivative of the function. y = In(e2x + 3)
Consider the bivariate function f(x.y) = (x + y)/3 for 0< x< 1 and 0<y< 2 and f(x.y) = 0 3. otherwise. (a) Show that f(xy) is a density function. (b) Find the probability that both X and Y are less than one. (c) Find the marginal densities of X and Y and show that they are not independent. (d) Find the conditional density of X given Y when Y = 0.5.
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+
Q2.Find the derivative of the following functions: 6 point a) y x5*x7 b) y 1/x-5 c) y = (-)8x6 d) y x.logx
6. A) Is the function y = |x + 5 continuous at x = -5? wh B) is the function y = |x + 5| differentiable at x = -5? why? 7. Use the rules of differentiation to find the derivative of the following functions. A) y = ln(2x + +5x + 7) B) y = tanx - COS X C) y = - - 355 D) y -
5. [12 Marks) Consider the level surface of the function f(x, y, z) defined by f(x, y, z) = x2 + y2 + x2 = 2a?, (1) where a is a fixed real positive constant, and the point u = (0,a,a) on the surface f(x, y, z) = 2a. a) Find the gradient of f(x, y, z) at the point u. b) Calculate the normal derivative of f(x, y, 2) at u. c) Find the equation of the tangent plane...
Re Consider the function y-932 dy a) Compute the derivative of this function. Do not include =in your answer. (6 Marks) dr 2y b) Compute the second derivative of this function, Do not include 2 3 in your answer and DO NOT factorise your answer. (6 Marks) dr 47
Re Consider the function y-932 dy a) Compute the derivative of this function. Do not include =in your answer. (6 Marks) dr 2y b) Compute the second derivative of this function,...