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- Suppose that y is a differentiable function of x andz = cos (x4y9).Express dz dx in terms of x, y, and dy dx Pick the correct form for the derivative and fill in the blanks for A, B, C, D, E, F, and G. dz/dx = sin (x4 y9) (A xB yC + D xF yG dy/dx) dz/dx= −sin (x4 y9) (A xB yC + D xF yG dy/dx) dz/dx= cos (x4 y9) (A xB yC + D xF yG dy/dx) dz/dx= −cos (x4 y9) (A xB yC + D xF yG dy/dx) whereA = B = C = D = F = G =Suppose z is given implicitly by the equation ln (yz2) + x3z = 1 in a neighborhood of the point P (1, 1), in which z = 1. The value of the directional derivative of z at P in the direction of the vector w = (1, −1), corresponds to:Suppose z is given implicitly by the equation ln (yz2) + x3z = −1 in a neighborhood of the point P (1, 1), in which z = −1. The value of the directional derivative of z at P in the direction of the vector w = (−1, 1), corresponds to: the answers are in the first attached image
- Show that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation =030. If E 200 cosh 2x sin 2y a,+ 200 sinh 2x cos 2y a, V/m, find the equation of the di- rection line passing through the point P(1,0,0) and sketch it in the z-0 plane for 0 < x < 5 and 0 < y < /4.Find the partial derivative of z with respect to u, if z = x^4+x(^2)y, x = s+2t-u and y=stu^2, when s=4, t=2, and u=1.