Question

In: Math

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!

Expert Solution

Consider the given function

For evaluating th partial derivative of 'f(x,y,z) ' with respect to x we need to consider only the variable terms involving x while fixing y and z as constants. So

here both are considered as constants

In general

hence

now on finding the second partial derivative

Similarly we can find partial derivative with respect to y as follows

on finding its second order partial derivative

Now consider partial derivative with respect to z

On evaluating its second derivative

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).

Find the four second partial derivatives. Observe that the second mixed partials are equal. z =...

Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 25xey − 8ye−x

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=?

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

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).

f is a twice differentiable function and that itssecond partial derivatives are continuous.Let h(t)...

f is a twice differentiable function and that its second partial derivatives are continuous. Let h(t) = f (x(t), y(t)) where x = 2e t and y = t. Suppose that fx(2, 0) = 3, fy(2, 0) = 2, fxx(2, 0) = 4, fyy(2, 0) = 3, and fxy(2, 0) = 1. h'(t) = fx * 2e t+ fy find h''(t) when t = 0. (I don't understand how for the second partial derivative d/dy (fy) = d/dt (x) *fyx...

Find all second order derivatives for r(x,y)=(xy)/2x+5y. (I need most detail at the rx/ry to rxx/ryy...

Find all second order derivatives for r(x,y)=(xy)/2x+5y. (I need most detail at the rx/ry to rxx/ryy part, I can't get the top correct)

Practice differentiating the following funtions in general and specific terms. Find first derivatives and second derivatives....

Practice differentiating the following funtions in general and specific terms. Find first derivatives and second derivatives. Compare your solutions using the general functions with that of the specific functions. Provide an economic interpretation for each derivative along with its sign. 1. Utility functions: a. U = f(x1 , x2 , x3) b. U = x1 x2 x3 c. U = (x1 x2 x3)2 2. Production functions: a. Q = f(K, L) b. Q = K.5 L.5 c. Q = aK.1 L.9 3....

Suppose the first and second derivatives of f(x) are: f' (x) = 4x(x^2 − 9) f''(x)...

Suppose the first and second derivatives of f(x) are: f' (x) = 4x(x^2 − 9) f''(x) = 12(x^2 − 3). (a) On what interval(s) is f(x) increasing and decreasing? (b) On what interval(s) is f(x) concave up and concave down? (c) Where does f(x) have relative maxima? Minima? Inflection points?

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