f (x, y) =x +y +2xy. [Hint: If the second partial test is inconclusive, find another way to classify the extrema.]

Q: Taking Clairaut's Theorem into account, how many different partial derivatives of order 5 does a…

A: Given query is to find the numer of possible partial derivative.

Q: Find critical point (0,0) of f(x,y) =e^[(-2x^2)+(3y^2)] is a min, max, or saddle point using the…

A:

Q: Find all the second partial derivatives. f(x, y) = x^y – 3xSy2 fxx(x, y) fyr(x, Y) %3D

A: Given: f(x,y)=x4y-3x5y2

Q: Find both first partial derivatives. h(x, y) = e-(x10 + y10) h,(x, y) = hy(x, y) =

A:

Q: Find the first partial derivatives. (x, y) = xFye-5y ,(X, Y) = ,(x, V) =

A:

Q: 3. Integration by parts: 3x d x (V3 2x+4

A: To find out the integration.

Q: Find the first partial derivatives with respect to x, y, and z. 7xz x+y

A: This question is related to differentiation, We will solve it using given information.

Q: Find the first partial derivatives with respect to x,y and z. f(x. y.z) - 3x°y - 9 xyz + 10 yz %3D

A: Find first partial derivative The derivative of xn with respect to x is given by  ddxxn=nxn-1

Q: f(x, y) = x³ + y3 - 3x2 + 12y2 + 3x + 48y + 70 relative maximum of f(x, y) at (x, y) = relative…

A:

Q: Find all the second partial derivatives. x, V) = x^y% + 2x5y x, v) = II

A:

Q: Find the first partial derivatives with respect to x, y, and z.…

A: w=7xzx+y Partially differentiating with respect to x, we get ∂w∂x=∂7xz∂x·x+y-∂x+y∂x·7xzx+y2…

Q: Differentiate implicitly to find the first partial derivates of z z = e* sin(y + z)

A:

Q: Determine the Integrating factor of the DE: y (x³e*y y) dx + x (y + x³e*y) dy 3 1

A:

Q: Consider f(x,y) =x'+y* +2ry-x+5. Find its critical points and use the second partials test to…

A:

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x?y – 3xyz + 8yz?…

A:

Q: Find the critical points, relative extrema, and saddle points of the function. (If an answer does…

A:

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 5xyz + 10yz?…

A: Topic-partial derivatives

Q: J(X) = -3|X – 5| + 2 1. Why does J(X) have a critical point at X = 5? Explain. 2. Why does J(X)…

A:

Q: Use the second partials test for relative extrema to f. Find critical point (0,0) of f(x,y)…

A: To find: The maximum value, Minimum value, saddle point using second partial derivative test.

Q: 3x + x-10 OHence, evaluate dx by first expressing the integrand as sum of partial x2 +4x+4…

A: Explanation of the answer is as follows

Q: 4 f(x,y) = x² – 4xy + - 1. Find all critical points and use the second partials test to classify…

A: We use partial derivative to solve this Question

Q: ompute the partial derivative: (1, y) = cos(x+ – 6y) -(0, т) —

A:

Q: The linearization of ex at x = 0 Derive the linear approximation ex = 1 + x at x = 0.

A: Given, ex ,x=0 We know that, The formula for the linearization is, Lx=fa+x-af'a

Q: y" + 4y' + 3y = 0, y(0) = 2, y(0) = -1

A:

Q: Find all relative extrema/saddle points with second partials for the function…

A:

Q: f(x,y)=sqrt((x-3)2+(y+8)2+4)) compute the first partial derivatives of f(x,y) fx(x,y)= fy(x,y)=…

A:

Q: The partial differential equalion formed to om the (x -af + ÿ +(2-65 = 16 is nelation 9. %3D = 16

A:

Q: Consider the model of two competing populations defined by (dx = x(2 – 0.4x – 0.3y) dt |dy - = y(1 –…

A: Sol

Q: Find the partial integral. gy Y dx /1

A: y will behave as constant

Q: Find the first partials of cos (x° + y°) fa (x, y) = fy(x, y) =

A:

Q: %3D MUTM az əz +y= əz X- dv ay TTM UTN

A:

Q: (2y° + xy }tx + (x*y² – 2}ty = 0 Integrating factors found by inspection: %3D

A:

Q: Find the critical points and test for relative extrema. List the critical points for which the…

A:

Q: Find the first partial derivatives of the function. f(x, y, z) = xz – 7x3y3z6 fx(x, y, z) fy(x, y,…

A:

Q: (x In 2x dx = u v- Jv du -Svdu- Using Integration By Parts, Fand uv- fvds uv- Jvau 3 3 xVX In 2x-V지…

A:

Q: Find the value of x which minimizes: 1 Use the Lagrangian method = [x*)dt min. J s.t. X 3D —2х +4…

A: Given: J=∫01x2dts.t.x˙=-2x+4x0=1x1=0

Q: both first partial derivatives. z = exy %3D az %3D ax %3D ay

A: Solve above problem.

Q: FIND THE PARTIAL DERIVA TIVES OF z = x cos (y- x )

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: (a) Find the first partial derivatives of f(x, y) = cos(2.ry) – e³y+2x. (b) Evaluate (0,0) and (T,…

A:

Q: y= 0, y(1) = 1, y(1) = 0

A: We have to solve given problems

Q: 13. Find the four second partial deriv h(x,y) =x° +xy° + 9 + xy дудх дхду

A: Solve the following

Q: Find the partial integral. 5y Y dx

A: Given, The partial integral ∫15yyxdx We have to evaluate the partial integral.

Q: evaluate using partial functions *IntegralSymbol* 1/[(x+a)(x+b)] dx

A:

Q: Find the first partial derivatives. = x° – 9y Əz Əx Əz ду II II శశ శీ

A: Differentiate with respect to x  And y

Q: 2. Reverse the order of integration of S Saz dxdy. y+2

A: The objective is to reverse the order of integration

Q: Find the integrating factor of : 2y(x2 - y+ x )dx + (x² – 2y)dy = 0 ху O y 2х e2x

A:

Q: Find the first partial derivative wx, wy, wz of ( x  +  yw )2 –  ez  – 2 = 0

A: Let's find partial derivative of given function.