Compute d/dx f ( g (x)), where f (x) = 4/x+ x2, g (x) = 1 - x4

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

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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 d2y/dx2 by implicit differentiation x3 + y3 = 1

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Q: Solve the first derivative of f(x) = e-2x In x at x 0.5 using forward finite-divided difference and…

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

Q: A second derivative Findd2y/dx2 if x2 + y2 = 1.

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Q: Find dy/dx by implicit differentiation. xy + 5x + 2x2 = 3

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Q: Compute dy/dx using the limit definition of the first derivative for f(x) = 3x2

A: Given function is f(x)=3x2. we have to find the derivative using limit definition .

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

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Q: Find dy/dx by implicit differentiation. 52) x3 + y3 = 5

A: Given implicit function : x3+y3=5

Q: The derivative of f(x) = 5x – Vx + (sin)x – e² -

A: Given; f(x)=5x4-x1/3+[sin(π/2)]x-e2

Q: Find - by implicit differentiation. dx = y² + 2 x + y dy dx

A: differentiate wrt x

Q: Find the derivative of the function. rcos(x) y = In(1+2t)dt sin(x)

A: Applying Leibniz rule

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

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Q: 2x2+x dx x+1

A: Integration ∫2x2+xx+1dx

Q: Find dy/dx by implicit differentiation. x2 + y2 = 9

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Q: Find dy/dx by implicit differentiation. 9x3 + x2y - xy3 = 1

A: Given that: 9x3+x2y-xy3=1

Q: Solve the first derivative of f(x) = 52x+1 at x = 0.5 using backward finite-divided difference and a…

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Q: x* + x²y² + y³ = 5

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Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

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Q: Compute the derivative of the function y=x2/ln x at x=e.

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Q: Find the second derivative of f(x) = x2+ e* - COSX. O a. f(x) = 2x + xex - cosx O b. f'(x) = 2x + e*…

A: Solve by derivative

Q: Find dy/dx by implicit differentiation   x2 + 5x + 9xy - y2=4

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Q: Calculate the 4th derivative of the function y=x2/x−1 at x=2.

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Q: Find the derivative. [미 In dx x +3 x-3

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Q: Can you help me with this problem step by step?

A: The given equation,

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

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Q: 4. FIND d²y BY IMPLICIT DIFFERENTIATION: x² + y² = 81 %3D dx2

A: Given: x2+y2=81

Q: Compute all second derivatives of f(1.y) = (x+) e- %3D

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Q: Find dy/dx by implicit differentiation. x²y³ -yax dy/dx =

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Q: 6. Find the first order derivative with respect to z of the function u = In/x2 + y2 +z²

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Q: Compute the derivative: x4 – 4 d - at x = 2 dx x2 – 5 - The derivative is:

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

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Q: Find y" by implicit differentiation x2 5y2 5 + = 2 X у"-

A: Take d/dx on both sides and distribute it on the left side. Derivative of constant =0

Q: 5. Find the first order derivative with respect to y of the function U = In/x² + y² + z²

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Q: у %3D V1+ 2х (1 — х)-3

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Q: F(x) = "(5t - 1) dt %3D

A: We need to find the first derivative of F(x)=∫x2x(5t-1)dt. By Leibniz's integral rule,…

Q: (a) By using the chain rule and the derivative if x>0 (1, -1, if x< O' d (\xl) = dx | d find - (lx3…

A: Just break the mod function in two parts and easily calculate the derivative.

Q: 4. F(x) = (1-t) dt

A: To find the first derivative

Q: Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

A: First find the linear equation at x=1  then find the approximate values

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 derivative of the function. 5/1 x+1 In 22 + arctan x %3D X -1· dy dx

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Q: Find the derivative. 8) y = (x + 1)2(x2 + 1)-3 dy dx dy = -2(x + 1)(x2 + 1)-4(2x2 + 3x – 1) A) B) Y…

A: We can find the correct answer as below.

Q: find dy/dx by implicit differentiation x2 + xy + y2 - 5x = 2

A: Given: The implicit function x2+xy+y2-5x=2 The given function can be differentiated by…

Q: Find dy/dx by implicit differentiation. x4/3 + y4/3 = 1

A: Given that: x4/3+y4/3=1

Q: 19. Determine the derivative of f(x) = e* coshx. O a. e2x O b. ex O c. e4x O d. e5x

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Q: 5. Find derivative of the following composite function using the Chain Rule: f(x) = 3x2 + 8x, x(t) =…

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Q: Show that the derivative of f(x) =xln(x)−x is ln(x). Use this to compute∫ln(x)dx.

A: Sum/difference rule of differentiation,

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

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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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