1a) Find all first and second partial derivatives of f(x,y)=x^4−3x^2y^2+y^4 1b) w=xycosz, x=t, y=t^2, and z=t^3....

1a) Find all first and second partial derivatives of f(x,y)=x^4−3x^2y^2+y^4

1b) w=xycosz, x=t, y=t^2, and z=t^3. Find dw/dt using the appropriate Chain Rule.

1c) Find equation of the tangent plane and find a set of parametric equations for the normal line to the surface z = ye^(2xy) at the point (0, 2, 2).

Expert Solution

please comments if you have any problems

milcah answered 2 years ago

1) Find all of the second partial derivatives of f(x,y)=3(x^4)y-2xy+5x(y^3). 2) Find an equation of the...

1) Find all of the second partial derivatives of f(x,y)=3(x^4)y-2xy+5x(y^3). 2) Find an equation of the tangent plane to z=32-3(x^2)-4(y^2) at the point (2,1,16).

Calculate the all of the second order derivatives of f(x,y)=x^4 y- 〖3x〗^4 y^3+5y-10 Let be f(x,y,x)=2x^5...

Calculate the all of the second order derivatives of f(x,y)=x^4 y- 〖3x〗^4 y^3+5y-10 Let be f(x,y,x)=2x^5 yz^3-3x^(-4) y^3 calculate the f_xyz=? If f(x,y,z)〖=5e〗^(-xyz^6 ) +lnx calculate the f_yxz=? Let f(x,y)=cos(x^3 y) ise df/dx=? df/dy=? z=2x+y , x=sin(3t ) and y=cos(3t) using the chain rule calculate the dz/dt where t=π/2. Find the critical points of the f(x,y)=〖6x〗^2+12y^2+12x-24y and provide the information about the critical points obtained (if it is max, min or saddle point).

need calc 3 assistance!! Find all second partial derivatives of f ?(?, ?, ?) = (?^?)(?^?)(?^?)...

need calc 3 assistance!! Find all second partial derivatives of f ?(?, ?, ?) = (?^?)(?^?)(?^?) pls show work and explain thank u!

Find the first-order and second-order partial derivatives of the following functions: (x,y) =x2y3

Let z=e^(x) tan y. a. Compute the first-order partial derivatives of z. b. Compute the second-order...

Let z=e^(x) tan y. a. Compute the first-order partial derivatives of z. b. Compute the second-order partial derivatives of z. c.∗ Convert z = f(x,y) into polar coordinates and then compute the first- order partial derivatives fr and fθ by directly differentiating the com- posite function, and then using the Chain Rule.

1. Find the partial derivatives of f(x,y) = xe^(4xy) fx=? fy=? 2. Find the partial derivative...

1. Find the partial derivatives of f(x,y) = xe^(4xy) fx=? fy=? 2. Find the partial derivative of f(x,y) = sqrt(x^3 + 4y^5) fx=? fy=?

1. a. Find the relative maximum and minimum values of f(x, y) = (3x^2) − (2y^2)...

1. a. Find the relative maximum and minimum values of f(x, y) = (3x^2) − (2y^2) b. Find the relative maximum and minimum values of f(x, y) = (x^3) + (y^3) − 6xy . The expression that you may need D = fxx(x0, y0)fyy(x0, y0) − (fxy(x0, y0))2

Compute the first partial derivatives of h(x,y,z)=(1+9x+4y)^z

T/F and why(true/false)? (Part a) If the partial derivatives fx(x,y), fy(x,y) exists for all values x,y...

T/F and why(true/false)? (Part a) If the partial derivatives fx(x,y), fy(x,y) exists for all values x,y ,then f(x,y) is continuous. (Part b) Suppose f(x,y) is a function which is differentiable and nonnegative everywhere, and is zero at the origin ,f(x,y) ≥ 0, f(0,0) = 0.Then the gradient vector is zero at the origin is,∇f(0,0) = (0,0). (Part c) If F(x,y) is continuous on the entire plane, then there is a function f:R→R satisfying f′(x) =F(x,f(x)), f(0) = 0 for all...

Define f : Z × Z → Z by f(x, y) = x + 2y. (abstract...

Define f : Z × Z → Z by f(x, y) = x + 2y. (abstract algebra) (a) Prove that f is a homomorphism. (b) Find the kernel of f.

Question