* 0 ☆ T 7.3. Show that (a). f(z) = x - iy² is differentiable only at y = -1/2 and f'(z) = 1, (c). f(z) = yx + iy2 is differentiable only at x = y = 0 and f'(z) = 0,
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- Suppose f is a differentiable function of x and y, and the following applies. p(t) = f(g(t), h(t)) g(3) = 6, Find p'(3). p'(3) = g'(3) = -5 h(3) = 7, h'(3) = 8 h'(3) fx(6, 7) = 6, f,(6, 7) = 5Differentiate. 7t f(t) t3 - t - 1 f'(t) =b) Consider the second-order truncation error (0 (Ax)²) with the step size (-Ax) and then, obtain a finite difference approximation for the first-order derivative of U(x, t) respect x (Ux(x, t)).
- A function H is differentiable at x = 2. An equation for the line tangent to the graph of H at x = 2 is 3x + 3y = 3. Find H(2) and H' (2). H(2) = H' (2) = 0 O Dointsl DETAUSSuppose that y and z are twice-differentiable functions of x. Show thatThe derivative of f(t) = 21° · h(t), where fand h are differentiable functions is: A. 10r° · h(t) + 2° · h'(t) B. 10r* - h'(1) C. 101* · h'(1) + 2° · h(1) D. 10r* - h(t) + 2r - h'(1) 5. O A. OC. D. 3.
- Suppose that z=f(x,y) is a differentiable function of x and y with (1,2)= 4, ze (1,2)=2. If x=x(t) and ду y=y(t) are differentiable functions of t, with x(0)= 1, y(0)= 2, x'(0)= and z'(0)=2., find y'(o). 2 1 %D %3DThe total derivative of the function f(x,y) =2x²y – xy is a. df = (2x* - x)dx + (4.xy – y)dy b. df = (4x – y)dx +(2x² – x )dy c. df = (4xy – y)dx +(2x² – y)dy - d. df = (4xy – y)dx +(2x² – x )dyA cylindrical vessel without lid is 4 cm in radius and 10 cm in height. If the vessel is to be coated with 0.4 cm of silver, use differentials to approximate the amount of silver to be used. Let z be a differentiable function of r and y related by the following equation: Əz Find at the point (3,0,0). ду x+z x-z = (√y + cosh(z))².