Find y as a function of x if x'y" – 9xy' + 25y = x", y(1) = 2, y'(1) = -5. y =

Q: Find the derivative using the theorems on derivatives. dx x2-2 1 y = 2.y = (x² – 1)³(x² + 3)² x3+4x…

A: Given functions to be differentiate are    1.   y=x2-2x3+4x    3.  y=x2-2x      we will make use…

Q: Find the partial derivative. z = sin(9x°y – 10xy²)

A: Given: z=sin9x3y-10xy2

Q: Find y' by implicit differentiation 1. x³+y³=6xy 2. x²+y²=4

A: 1. Given: x3+y3=6xy To find y'by using implicit differentiation the implicit differentiation is…

Q: Find the derivative of the function f (x, y) = x²y + y²z: at Po(1,2,3) in the direction of û = 2î –…

A: To find the derivative of the function f(x,y)=x2y+y2z at P0(1,2,3) in the direction of…

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

A:

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: In xy = x² + sin xy

A:

Q: find dy/dx of each equation using implicit differentiation. a. y4 -2y2x2 + 3x2 = 0 b. (x + y)3 =…

A:

Q: Determine the differential of the function y=x3−3x2+4x at the point x0=1 when dx=0,1.

A:

Q: Find the differential dy of the given function y=extanx

A:

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

A: Implicit partial differentiation

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

A: Given the function:

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

A:

Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…

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

A:

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: ,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: find the partial derivative of the function with respectto each variable. ƒ(x, y) = 1/2 ln (x2 + y2)…

A: The given function is fx,y=12lnx2+y2+tan-1yx.

Q: Find the differential d8y of the function y=exsinx.

A:

Q: find y' by implicit differentiation. ex/y=3x-2y

A: To find the derivative of the equation using implicit differentiation.

Q: Find the first three derivatives of y = x(In x)³

A: given problem :y=xlnx3

Q: If f(x, y) = ln(x + y), then total derivative or total differential of f at x = 3 and y = 20 is : Y

A: Given data: The given expression for the function is f(x,y)=ln(x+y). The given value of x is x=3.…

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

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Q: Find by implicit differentiation for x2+y2=25 at point P(0,5).

A:

Q: Compute the indicated derivative using the chain rule. X = 4 + 3t, y = -7t; Oy

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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: Find the derivative of y with respect to x. y = tan 1 (In 4x) 1+ (In 4x)2 xV1+ (In 4x)² x(1 + (In…

A: We will find the derivative of y with respect to x as following.

Q: Find the nth-order differential of the function y=2x.

A: To find nth order differential of the given function.

Q: Get the first order derivative of the function x + sin(y – 2x) - 1= 0 - 2 1 a. y' = cos(y-2x) 1 b.…

A:

Q: Use the appropriate form of the chain rule to find the derivatives. 12x2 + 12y2 + z²; x = p sin o…

A: Given:  w = 12x2+12y2+z2 x=ρ sinϕ cosθ, y=ρ sinϕ sin θ, z= ρ cosϕ  Find: ∂w∂ρ, ∂w∂ϕ and ∂w∂θ Chain…

Q: Find the derivative of y with respect to X. y = tan 1 5x 105x(1 + 5x) 2(1 + 5x/5x J1- 5x 1+ 5x

A: It is derivative.

Q: If we are getting the partial derivative of f(x,y) with respect to x, we are letting the y variable…

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

A:

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: Find the differential of the function. u = 2x +

A:

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: b) Find derivative of the following: 1. y= 5x° + 2x -x + x* -9x+12 y=1-cos 20+3sine iI. ii. s= xln…

A: The detailed solution is as follows below:

Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

Q: Find the derivative of y with respect to z. y In (sinh 3z) y -

A:

Q: Find y″ by implicit differentiation. x2 + xy + y2 = 8

A: Given:    Implicit differentiation :     x2+xy+y2=8   differentiating on both sides we get…

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: 23-4z2-2一4 y = %3D 1+ Va

A:

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

A:

Q: Find the third order derivative of y = In(cos(2x))". A. y' = -40sec²(2x)tan(2x) B. y' = -80sec…

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Q: Find y'' by implicit differentiation. 5x2 + y2 = 4

A: Implicit differentiation

Q: Find the derivatives of the f: 1. y: sin (x²+3) 6. y= e tan 3x 7. y: e 2. y= tan (4x*) cot (3x-8) 3.…

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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 y'' by implicit differentiation. x2 + 4y2 = 4 y'' =

A: The detailed solution is as follows below:

Q: Find the derivative of the function. (x-7)(x²+2x) +3 y = O A. OB. dy dx O D. dy dx dy O C. dx dy dx…

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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…