Find the linearization of the function f (x) = x' at x = 1. L (x) =

Q: Form the partial differential equation by eliminating the arbitary from z=xy+f(x2+y2)

A: Form the partial differential equation by eliminating the arbitary from z=xy+f(x2+y2)

Q: Compute the indicated derivative using the chain rule. x = 6 + 3t, y = −8t;  dy dx

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Q: Find the differential of the function: y = x In x

A: Solution:Giveny=x ln xTo find the diffferentiationformula:(uv)'=uv'+vu'ddxxn=nxn-1ddxln x=1x

Q: Find the differential of the function. Y = e2x

A: Given function is  y= e2x

Q: Find the second derivative d2y/dx2 of the implicit curve y3=xy+1  at (0,1)

A: y3 = xy +1differentiating both wrt to x3y2dydx= y+xdydx+0dydx3y2=ydydx= y3y2-x

Q: Find the maximum rate of change of the function f(x,y) = sin (xy) at the point (4,0) and the…

A: The given function is f(x,y)=sin (xy) and the point is (4,0)=(a, b). to find : Maximum rate of…

Q: Find the differential of the function y=√x3+4x at x=2.

A: Given the function:

Q: Use Leibniz’s Rule to find the derivatives of the functions

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Q: Calculate the differential of the function y=x5−7x3+5x at the point x=2 when dx=0,2.

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Q: From the partial differential equation by elimanating the arbiraty function z=f(x2+y2+z2)

A: We have to form the partial differential equation.

Q: Find the partial derivative of the given In[y? sec(x²y²)].

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Q: Compute the indicated derivative using the chain rule. dy x = 5 + 3t, y = -8t; dx dy %3D dx

A: We have to find the indicated derivative by using chain rule: x=5+3t, y=-8t Differentiating first…

Q: Compute the derivative: 3 | Vsin t dt dx

A: To find ddx∫x3sin t dt We know that, ddx∫u(x)v(x)f(t) dt = f(v(x))v'(x)-f(u(x))u'(x) Then, we have,…

Q: ,2x Calculate the second derivatives of function f(x) = sin(x) + Ide²x at point x = 0.625 using…

A: Three point central differential formula for 2nd derivative   f′′(x)= f(x-h)-2f(x)+f(x+h)h2 Five…

Q: COs X Compute the mixed second order partial derivative of z =

A: The mixed second order partial derivatie of z=cos x y5  is given by ∂2z∂x∂y=5sin xy6

Q: y = Arctan√3x−4/4 2. y = 2 Arccos ( 1 -x/2) + √4x − x2 3. y = ln (x3(x−1)/(x−2)^2) 4. y…

A: d2dx2arctan3x-44=d2dx2arctan3x-42=ddx1x3x-4=-9x-82x23x-43x-4…

Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

Q: Calculate the differential of the function y=2x x2−3 at the point x=3 when dx=−315.

A:

Q: The linear Differential equation of any order if there is no constant term s present is known as?

A: We have given The linear Differential equation of any order if there is no constant term s present,…

Q: Find partial derivative of dx for the function f(x.y) given below exp 2x. siny .(at the point (In2,…

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Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ?

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Q: Find the differential d3y of the function y=xsinhx.

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Q: Form the partial differential equation by eliminating the arbitary function from z = xy + f(x² +y°)

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Q: Use central difference approximations to estimate the first and second derivatives of y = e* at x =…

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Q: Obtain the differential equation of the family of straight lines with slope and y-intercept equal.

A: Equation of straight line: y=mx+c Where, m = slope  c = y-intercept

Q: Form a differential equation by eliminating arbitrary Function. Z= (x + y)f(x² + y² ) %3D

A: Given z = (x+y)f(x2+y2)zx+y = f(x2+y2)                             (1) Partially differentiate with…

Q: a differential equation is classified as a homogeneous DE if one can directly isolate all functions…

A: A differential equation is classified as a homogeneous DE if one can directly isolate all functions…

Q: Find the derivative of the function.

A: Given: y=ln(x4)(1,0)

Q: Find the differential of the function y=xxe2x at the point x=1.

A:

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: Find the differential of the function y=2x2+3x+1 at the point x=1 when dx=0,1.

A: To find the differential of the given function at point x = 1 when (d x) = 0, 1.

Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8

Q: Find the first-order partial derivative with respect to x of f(x,y) = e5x siny.

A: To find the first-order partial derivative with respect to x, given function, fx,y=e5x sin y

Q: Form the partial differential equation by eliminating the arbitary function from z=xy+f(x2+y2)

A:

Q: Find the solution of non linear partial differential du equation ди = U бу dx

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Q: (a) Find the first derivative of the function y= la) with respect to x by using the chain rule.

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Q: a. Obtain the differential equation of the family of straight line with the algebraic sum of the…

A: Write general equation first of given conditions.

Q: Calculate the second-order partial derivative of f(x.v) =sin(x³v?) with respect to x and y, that is,…

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Q: Compute the derivative of x(x + 2) (2x + 1)(3x + 2) y = (a) directly using the Chain and Product…

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Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

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Q: Find the derivative of the function. 1 g(x) = dt Jtan(x) V2 +

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Q: Use Leibniz’s Rule to find the derivatives of the functions

A: Given: y=∫x22x2lnt dt

Q: 8. Find the derivative of y = In(3t) dt.

A: To Determine: Find the derivative of given integral:…

Q: Find the 1st and 2nd derivative of: Vx + Jy = va

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Q: Find the gradient of the tangent to the curve xy“ + y+ ( log_(x – 2))² = 14 at the point (3, 2).

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Q: What is the integrating factor of y' - 2xy x?

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Q: Calculate the derivative of the function g(x)=x∫√x(t2−t)dt at x=1.

A: using the fundamental theorem of calculus we find g'(x)

Q: Calculate the increment and differential of the function y=x2−x+1 at the point x=2 when dx=1.

A: Given, the function is y = x2 -x +1 at the point x = 2 and dx = 1, We have to calculate the…