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

Find the first-order and second-order partial derivatives of the following functions:

(x,y) =x²y³

Expert Solution

Z = f(x, y) = x²y³

(1) First-order partial derivatives are:

Zx = Z/x = 2xy³

Zy = Z/y = 3x²y²

(2) Second-order partial derivatives are:

Zxx = /x(Z/x) = 2y³

Zyy = /y(Z/y) = 6x²y

Zxy = /y(Z/x) = 6xy²

Zyx = /x(Z/y) = 6xy²

Rahul Sunny answered 2 years ago

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 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).

Write down expressions for the first-order partial derivatives, ?z and ?z for ?x ?y (a)z=x2 +4y5...

Write down expressions for the first-order partial derivatives, ?z and ?z for ?x ?y (a)z=x2 +4y5 (b)z=3x3 ?2ey (c)z=xy+6y (d)z=x6y2 +5y3

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).

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=?

Evaluate the required second order partial derivative. Find fyx(4, -1), if f(x, y) = -4x3y2 +...

Evaluate the required second order partial derivative. Find fyx(4, -1), if f(x, y) = -4x3y2 + 2x4 - 3xy3. Group of answer choices 759 768 375 502

Consider the homogeneous second order equation y′′+p(x)y′+q(x)y=0. Using the Wronskian, find functions p(x) and q(x) such...

Consider the homogeneous second order equation y′′+p(x)y′+q(x)y=0. Using the Wronskian, find functions p(x) and q(x) such that the differential equation has solutions sinx and 1+cosx. Finally, find a homogeneous third order differential equation with constant coefficients where sinx and 1+cosx are solutions.

Question

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

Solutions

Expert Solution

Related Solutions