h(t)k'(t)dt = h(b)k(b) – h(a)k(a) – h'(t)k(t) dt .

Q: Find the second partial derivative for the function z = x7-7xy + 6y2 with respect to x.

A: Solution of given question is written in below steps.

Q: Differentiate implicitly to find the first partial derivatives of z                        tan(x +…

A: Here in the given question, it is required to differentiate implicitly to find first partial…

Q: Differentiate implicitly to find the first partial derivatives of z                              xz2…

A:

Q: 26) Find the partial derivative of of f= y cos x+ 2x sin z + 5y with respect to y.

A:

Q: Find the differential dy of the given function. y = In√9-x² dy =

A: Given y=ln9-x2 Formula: ddx(ln u)=u'u where u is a function of x Now consider y=ln9-x2 The given…

Q: If U = lx+my,v=mx-ly then prove that partial derivative of x

A: Given: u=lx+my v=mx-ly   To show: ux=-vy and uy=vx

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: Explanation- Given that, The initial value problem is- ydydx=x-1;  y0=1 By simplifying it further,…

Q: Is this polynomial, x In x – y In y - a homogeneous differential equation?

A:

Q: Find for the following equation by Implicit Partial Differentiation; дz x³ + y²z4 + 3xyz = 5

A: Implicit partial differentiation

Q: If f(x, y) = y² cos(x) – a° In(y), find the second partial derivative

A: Partial derivative problem

Q: z = x siny + y sinx

A:

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: Explanation-  Given that, The initial value problem is- dydx=x2-y2 ; y0=1 Here, The function is-…

Q: a?f (or and y. that is, f(x,y) = e² with respect to ayax axay Calculate the second-order partial…

A:

Q: If f(x, y, z) 2x5 + 3y5 - 8x2y2z2, what is the partial derivative of f with respect to z?

A: The given function is fx, y, z=2x5+3y5-8x2y2z2.

Q: (d) f (x,y) = ln (4x – 5y)

A: The given function is fx,y=ln 4x-5y. The second order partial derivatives are fxx, fyy and fxy.…

Q: 2. Let f(x, y,2) = z-sin(xy), x = t, y = In t, z = e. Find derivative of f directly and by using…

A:

Q: Use partial differentiation to find the derivative of the implicit function dy (3x'y-1)+ 7xy = 9…

A: We will use the given formula to solve this question.

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: Differentiate implicitly to find the first partial derivatives of z                              x2…

A: Given that function, x2 + y2 + z2 = 1 Differentiate with respect to x on both sides,…

Q: Differentiate implicitly to find the first partial derivatives of z…

A: the given implicit function is:xlny+y2z+z2=8

Q: 3. Write the exact differential: f(x,y)=e-y-el-

A: Given- fx,y=ex-y-ey-x To write the exact differential.

Q: Find the first partial derivatives of f(x, y) = 4x cos(x2 + y?). %3D

A: Given fx,y=4xcosx2+y2

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: The given initial value problem is ;    ydydx = x-1  with  y(1) = 0 We have to determine the…

Q: Find the first and second order partial derivatives for z x2 sin (3x + 2y).

A:

Q: Find the partial derivative. z = sin(2.a*y – 3xy?) az

A:

Q: €) Find the mixed partial derivative at the point h(x,y) cos (x)sin(y) ++xy

A: The derivative of a function f(x) with respect to x represents the rate of change of f(x) with…

Q: Find the first order partial derivative with respect to y S(x, y) = a"y² + 3ze"

A:

Q: If f is a function of x and y such that fxy and fyx are continuous, what is the relationship between…

A: Function: fx and fy are continuous function. Let us choose f(x,y)=x3y3+πxy Here fx=3x2y3+πy…

Q: Find the partial derivative of f(x,y) with respect to y at the point (3,2) f(x,y) = ln(x^2y-xy^2)

A: A partial derivative of a function of several variables is its derivative with respect to one of…

Q: Find all second-order partial derivatives for the following. f (x, y) = 2y ln x

A: To find all the second order derivative for the function f(x, y)=2ylnx

Q: find the first partial derivatives of the function f(x, y) = integral from y to x of cos(t^2) dt

A: the given function is , f(x,y)= ∫xycos(t2)dt

Q: Find the partial derivative of u=xy+yz+zx with respect to x.

A: Here, we need to find the partial derivative of u=xy+yz+zx with respect to x. So,              ∂ ∂…

Q: If f(x, y) = y cos(x) – x³ In(y), find the second partial derivative dy dx

A:

Q: Differentiate implicitly to find the first partial derivatives of z. z = (e^x) sin(4y + 7z)

A:

Q: If f(x, y) = y² cos(x) – x³ In(y), find the second partial derivative ду дх

A:

Q: Find the first and second order partial derivatives for z = x² sin (3x + 2y).

A: As we know that; The product rule: f·g'=f'·g+f·g' The chain rule: fgx'=f'gx·g'x And The first order…

Q: Given function f(x, y) = 1+ xy - x - y. df a) using partial differential involving limits to obtain…

A:

Q: Find both first partial derivatives. z = ln√xy

A: Given  z = ln√xy. We need to find both the first partial derivatives of the above function.

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

A:

Q: Consider the nonhomogeneous differential equa 1 "(x) + y(x) = e '+ sin a

A:

Q: If z = sin(x/y) and x = ln (u) and y = v^4, find the partial derivatives of z with respect to u and…

A:

Q: Let x and y be differential function of t and suppose they are related by the equatin xy-1=y^2. Find…

A: Differentiating with respect to t, we get

Q: z = x sin(xy)

A:

Q: A more detailed version of Theorem 1 says that, if the f f(x, y) is continuous near the point (a,…

A: Given: (15). dydx=x-y (16).dydx=x-y

Q: Consider the following function: z = α x+ β y^2, where alpha and beta are constant parameters. Write…

A: To find the total differential dz and partial derivatives.

Q: find the partial derivative of the function with respectto each variable. h(x, y, z) = sin (2πx + y…

A: We have to find the partial derivative of the function with respect to each variable   The given…

Q: (b) Find the partial derivative, g where g(x,y)=sin' (2x+y). (c) Given z= In(2x+3y) with x 2s' (t-s)…

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: