Find a function whose graph passes through the point (1,2/e) and satisfies x^2y'=y.

Q: Find dy/dx by implicit differentiation   2x3 +x2y  -xy3  = 2

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Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: If x+y divided by x-y= x^2+y^2 and dx/dt=12, then what is dy/dt when x=1 and y=0? show all work…

A: Given thatx+yx-y=x2+y2x+y=(x-y)(x2+y2)  [cross multiply]x+y=x3+xy2-x2y-y3

Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFf(x) = Vx+2.

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Q: Differentiate the function. y = etan(θ)

A: Given y=etanθ Use chain rule of differentiation to differentiate the given function.

Q: Find the first derivative: y= ln v5x3 –- 2 5, O y = 222 %3D 523-2 O y' = 322 5z3-2 O y' = 622 5z3-2…

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Q: Use implicit differentiation to find * az given that yz* + x²z3 = дх = exyz

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

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Q: Find  y ″  by implicit differentiation. 2x3 − 5y3 = 5

A: We will differentiate w.r.t x twice using the product rule and the chain rule

Q: Estimate ln(0.9) using a linear approximation

A: Given:ln(0.9)

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 indicated nth derivative of the following: 1 7. 2nd derivative of y = xArcsinx + v1 – x²…

A: Find derivative using product rule and composition of functions rule

Q: Estimate the root very near x = 0.4 of 4(x*)" - 4(x²) + 1 = 0 using the Newton- Raphson Method with…

A: Consider a function:  fx=4xx4-4x2x+1      =4x4x-4x2x+1

Q: FInd the derivatives of the function f(x) from the first pribnciple  cos2x

A: Derivative from first principal is ratio of change in y to the very small chance in x.

Q: #11, find dy/dx by implicit differentiation

A: Differentiate question 11

Q: Use forward difference approximation to estimate the first derivative of the following equation.…

A: Given that, fx=-0.15x3-0.2x2-0.5x+2.25h=0.5We need to find the first derivative of the function at…

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

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Q: Find  y ″  by implicit differentiation. 4x3 − 5y3 = 8

A: First we find y' by differentiating  both sides of the given equation. Then find y"  by using the…

Q: Find dy/dx by implicit differentiation at point (0, 0) if x³y³-y=x

A: Here, x3y3-y=x

Q: To compute fxyz, we first take the partial derivative with respect to which variable?

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Q: Find the derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

Q: Compute the second derivative of f(x)=ex+x at x = 1 using a step size h = 0.2

A: To find the second derivative of f at x = 1. The approximation formula for second derivative at a…

Q: Find dyydx by implicit differentiation. 1 + x = sin(xy2)

A: In implicit differentiation we differentiate the terms in LHS and RHS and then re-arrange the terms…

Q: Find both first partial derivative Z = 15x x/y az az ду

A: As we know that: The the Power law: ddxxn=nxn-1 From the given problem: z=15xy

Q: Find the function that passes through the point (1,2) and whose derivative is dy/dx = (2/x^3) - 4

A: Topic:- application of integration

Q: Compute the derivative: 4 te* dt d 3z2 L tet dz -1

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Q: Find a function with the given derivative whose graph passes through point P f'(x)= 2xx+1-cosx,…

A: To determine the antiderivative satisfying the given initial condition

Q: Please show me the partial derivatives for this homogenous equation and solve for GS/PS using Test…

A: Exact differential equation

Q: The GoldPlus Company determines that the marginal cost for their Aiibe 64GB flash drive is given by…

A: One of the methods to solve a differential equation is by separating the variables and integrating…

Q: Approximate the derivative of f(x) = x² + 4x + 5 at x = 3 using the forward, backward, and central…

A: f(x) = x2 + 4x + 5 h = Δx = 2 xi = 3         f(xi) = 26 xi+1 = 5          f(xi+1) = 50 xi-1 = 1…

Q: Find y''by implicit differentiation. 2x3 + 5y3 = 2

A: We can find y" using implicit differentiation as below.

Q: Find az when yz+x In y = 2.

A: Use implicit differentiation

Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFF (x) = Vx + 2.

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Q: Calculate the partial derivative * using implicit differentiation of exy + sin (3xz) + 2y = 0. (Use…

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Q: Integrate xtanx with respect to x

A: We have to solve this integral by  Integration by parts rule, Formula is  ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: Solve for the derivative of the function using chain rule. 7. f(x)= sin(e3x)

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Q: Solve for the derivative of the function using chain rule. 8. f(x)= sin (2x)cos (3x)

A: Given problem:- Solve for the derivative of the function using chain rule.   8.     f(x)= sin…

Q: Find the derivative of the function. InV y = In 6 - X %3D y' = %3D

A: Explanation of the answer is as follows

Q: Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.

A: solve the following

Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Find dy/dx by implicit differentiation. 3+10xv+4x-5x=0

A: Given

Q: Find dy ax oy Impticit dipTErentation 3. Find 2nd derivative

A: 1) The given equation is 2x2+2y2=17 Differentiate both sides of given equation 2x2+2y2=17 with…

Q: Find the 1st derivative of y= Arcsin x -v -V1-x²

A: To find the first derivative of y = sin-1x - 1-x2 sin y =x - 1-x2

Q: Find y'' by implicit differentiation 4x3+3y3=6

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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 any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x?

A: The given function: f(x)=x4-2x2 To find the first derivative of the function: f'(x)=4x3-4x Now, let…

Q: Consider the function f(x) = x³ Q 2: Calculate its first derivative at point x = 3 numerically with…

A: We have given , f(x) = x3

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

A: Given: y=∫x22x2lnt dt

Q: Find and sketch an exponential equation of the form y = Cekx that passes through the points (0, 8)…

A: Given an exponential equation of the form y=Cekx that passes through the points (0,8) and (3,4). To…

Q: (In iny

A: To find the derivative of the given function- lny=lnxylny Here we will use the following formulas-…