(b)* Show that Y' is closed.

Q: Find both first partial derivatives. z = 15XVY 15xVy %3D dz az

A: We need to find partial derivative.

Q: Find the firct derivatioves of the follwing: - 3 ) y= 3x-x -2 4) y: Jerx 2) y: Ji-7x 5) y = 2メ-3

A: ddxxn=nxn-1 ddxu(x)v(x)=v(x)ddx(u(x))-u(x)ddx(v(x))v(x)2

Q: Find both first partial derivatives. 18y2 x az %3D ax dz ду

A: The given function is:z=18y2x

Q: az Find if yz – In z = x + y ax

A: To find: The partial derivative ∂z∂x, if yz-ln z=x+y. Calculation: The partial derivative ∂z∂x can…

Q: Fina aly for y = 3x V3-x4

A: we have to find dy for given y

Q: Find both first partial derivatives.

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

Q: 2. 2. Let そニと X=UV, y = sin v, Use ナ chain chain Rule to find Ev.

A: 1) The given function z=e2x2y+3xy2 Differentiate with respect to x taking y as constant…

Q: Find both first partial derivatives. Z = In az %3D ax az ду

A: ∂z/∂x = 1/x    ∂z/∂y= -1/y

Q: Differentiate ysin(1/y)=1-xy

A:

Q: . Form the differential of the system of circles touching the y-axis at the origin.

A: The solution is given as

Q: Find the partial derivative. 17zy

A: Given, ∂xe17xy∂x We have to find the partial derivative.

Q: Find both first partial derivatives. 6y* az ду.

A:

Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: Find both first partial derivatives. z = 14y2Vx az ax az ду || ||

A:

Q: Find partial derivatives of x3sin y + cos2x tan5y with respect to x and y

A: We have to find the partial derivatives of  x3siny+cos2xtan5y with respect to x and y.

Q: Compute the partial derivatives: 6x dz az dy

A:

Q: Find both first partial derivatives. z = 13xy az az ду II

A:

Q: Find both first partial derivatives. 5xVy %3D az az ду

A:

Q: yUx-xUy=U , U(x,1)=2+e^-x

A: Given partial differential equation is, yux-xuy=u      .....1. With initial condition ux,1=2+e-x.…

Q: Find total differential of function u = x.

A: 6. The given function is u=xyz. We know that the total differential of a function u=fx,y,z is given…

Q: compute all the 1st and 2nd partial derivatives of x2 sin (x+y)

A:

Q: Find both first partial derivatives. z = exy

A: Given function is z=exy. Partial derivative of function means derivative of function with respect to…

Q: Find all the second partial derivatives. f(x, y) = ln(ax+by)

A:

Q: How is the Chain Rule applied when finding dydx implicitly?

A: According to the question, we have to explain the chain rule when used in the implict function.…

Q: Find all of the first partial derivatives: f(x,y) = y³sin(x) + x²tan(y)

A:

Q: Use chain rule to find given x² + 2y² + z² and x os (st), y %3D Cos

A: Solve the following

Q: Find both first partial derivatives. z = cos(10xy) az ax az ||

A:

Q: Give 1 problem of partial differentiation of function of U with respect to 3 independent variables…

A:

Q: Prove: cosh 3x = 4 cosh° x x-3cosh.x

A: Prove that :- cosh 3x=4cosh3 x-3cosh x

Q: Find the linearization of ƒ(x) = √(1 + x) + sin x - 0.5 at x = 0.

A: substitute 0 for x in f(x)=1+x+sin x-0.5 to obtain the value of f(x) at x=0 f(x)=1+x+sin…

Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

A:

Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

Q: 4. Find the first partial derivatives of the function. z= xsin(ry)

A: We will use the formula  (uv)'=uv'+u'v Given z=x sin(xy) Then the partial derivative with respect to…

Q: Compute the partial derivative of h(x, z) = e4xz-3x²z. (Use symbolic notation and fractions where…

A: In this problem first we need to partially differentiate the function with respect to z and then put…

Q: Find both first partial derivatives. Z = In

A:

Q: Find both first partial derivatives. z = 14y²Vx az ax az ду eBook

A: We have to find

Q: Find both first partial derivatives. az ax az ay

A:

Q: Use the Chain Rule to compute the partial derivative. би +о In (3u? + uv) = 3u + uv

A:

Q: Find the first partial derivatives of the funct f(x, y) = x8 + 7xy5 fx(x, y) =

A:

Q: Find the Linearizat ion of Non lineah Relations hip Y= (ax+

A: This is the problem of linearization, application of differential calculus.

Q: Find both first partial derivatives. z = 3xVy az ax az ду || ||

A:

Q: find all the second partial derivatives of Z and show complete solutions Z= tan-1 ( x2 / y3 )

A: Partial derivative of the function Z=f(x,y) is denoted as The first partial derivative∂Z∂x, ∂Z∂y The…

Q: Find both first partial derivatives. z = In() az дх az ду ||

A:

Q: What can you conclude about a real function f(x,y) that has continuous partial derivatives at a…

A:

Q: Give one problem for  partial differentiation of function of U with respect to 3 independent…

A: It is partial derivative problem

Q: Find both first partial derivatives in) z = az az ду

A:

Q: Find the partial derivative. 2 = (r² + 5z – 6y)“ az ||

A: The given function is: z=x2+5x-6y4