(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.
Consider the function g(x,y)=5.7sinx−7.9y2+8. Find the directional derivative of g in the direction v⃗ =(56) at the point P=(0,1). Answer:
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...