Find the linearization L(x) of the function at a. f(x) = sin(x), a = 3 L(x)

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

A: Given: z=sin9x3y-10xy2

Q: Part 4: A derivative computation using the FTC and the chain rule d d (F(2*)) = dx dt |3| e dx 20

A: Topic:- application of integration and derivatives

Q: * Part 4: A derivative computation using the FTC and the chain rule d d (F(x*) dx dt dx

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Q: dx Evaluate f- +1) using the Cauchy principal value.

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Q: Find the differential d4y of the function y=x5.

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Q: use implicit differentiation using partial derivatives to find: a) t for 2x?+3xy- 3y*= 2 b) for y…

A: Using the product rule of derivative, it can be written that ddx(xy)=xdydx+y .

Q: z = f( a, b, d, c), write the exact differential of the dependent variable

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Q: Find the local maximum, minimum and saddle points of the function using the second derivative test:…

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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…

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Q: 1 y = x²-1 Using differential, draw the function

A: This is a problem related to differentiation. Based on the general formula and concept we will…

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: (b) Find the first order partial derivative af and for the function f(x, y) = x/y –x²y+ y²

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Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: Given function is y=sin4 cosz. To find the derivative of the given functions. Solution: Chain rule…

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: fx=sin-1x,   a=π12 The value of the function and the value of the derivative can be easily…

Q: Find the derivative of the function at Po in the direction of A. 1- f(x, y) = 2xy - 3y² , Po ( 5,5),…

A: As per our guideline we are supposed to answer only one question you can repost other in next…

Q: Find the derivative of (a) (교2 + 1)" (6) In(cos²(e2")) 2x (c) sin-1 e-1 dt x +1 In a

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Q: dw of w -+ dt X y H.W: Use the chain rule to find the derivative dw with x= cos 1, y = sin? t, z =-…

A: We differentiate the function with respect to t.

Q: respect to x of/ /(3Vi-1) dt is 3x – 1 by the 2nd fundamental theorem of C The derivative with (A)…

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Q: let f(x,y)= z-sin(xy),x= t, y= lnt, z=e^t-1. find derivative of f directly and by using chain rule…

A: Plug the given expressions of x,y, and z. Then differentiate directly. And plug t=1

Q: Find the linearization of the function f(x) = sin(x) at a = π and use it to approximate the number…

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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= sin -3 O A. XV1-x - 3 O B. 1+x - 3x 3 c. 1-x -3 O D.…

A: Given that: y=sin-11x3

Q: b) Find O Using the chain rule to find de x-1 dy of y= dy of y sin 1-xy ) Using the implicit…

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Q: Shows the derivative function of: u³ + 2u, where u = x² + 3

A: Let's find.

Q: (a) Find the derivative. = In(x) – In(x - 8) dy dx (b) Find the derivative. y = In X - 8 dy dx %3D

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

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Q: Take first and second derivatives of y = xr, y=(ax2 + bx + c)2, y=ecx, y=e-cx, y=ln(x).  In all…

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Q: Find the normalizing constant c so that ce-x/4 dx = 1. C =

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Q: 1- Find the mixed partial derivative: w = e* +x In(v)+y ln(x)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 9. Find the derivative of the function using chain rule. f(t) = 3t In t

A: To find the derivative of the function

Q: 2] write the chain rule formula for the derivatives Of and E , where Z=ZCrisit).

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Q: If u, v, w are nonzero differentiable functions, then the first derivative of uv / w is

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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: Find the differential of the function.

A: Differentials are infinitely small quantities. We usually write differentials dx, dy, dt (and so…

Q: 04:- Use the Chain rule to find the derivative ) of z = 3x2 - 2 xy y and If x=x (u, v) = 3u + 2v and…

A: Please refer to the image below.

Q: Find the derivative of the function at Po in the direction of A. g(x, y) = x- (y/x) + V3 sec (2xy),…

A: we have to find directional derivative.

Q: Find the partial derivative with respect to x of e^y-2*ln(x)-x^3y^2.

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Q: Use the appropriate form of the chain rule to find the derivatives. 5.x2 + 5y2 + z²; x psin ф сos 0,…

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Q: (a) Show that the derivative solution of this function y = x** is x(x*+x-1) [1+x In x (In x + 1)] dx

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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: dw of w: dt x y Use the chain rule to find the derivative 1 with x cos t, y = sin t, z =- dw and…

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Q: Find the derivative of the function: y = In e+2*+1 Oy = x"[(2x(ln x + 1) + 1] y = x*(2 + x + x² In…

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Q: Let f(x, y,z) = z-sin(xy), x = t, y = In t, z = e4. Find derivative of f directly and by using chain…

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Q: the function f(x) = In 5x +3x + 13). 6. Differentiate ° 7. Find the derivative of the function .2 y…

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Q: Find all the second-order partial derivatives of the functions w = x sin (x2y)

A: Given function is w=xsinx2y. To find all the second-order partial derivatives of the function.…

Q: Assuming that the necessary derivatives of ƒ(x, y, z) are defined, how are Di ƒ, Dj ƒ, and Dk ƒ…

A: To find the relation between the directional derivatives Dif, Djf, Dkf with the partial fractions…