By direct differentiation of x(t) = eAtxo + eA(t-o) Bu(o)do show that ¿(t) = Ax(t) + Bu(t), x(0) = xo-

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: Evaluate the derivative of y = cos '2x - In 1-4x, where x = 0.125 -12> 2

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Q: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

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

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Q: Find the derivative of f(x) = In(x² + 1) %3D

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Q: Q1 Prove that the derivative of (2x +1) 2 is 4 (2x + 1) by using first principle derivative.

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Q: Find the derivative of the function y = (4x + 1)4(5x + 1)-5. dy (16x+4) 3 (4x+1)4 dx (5x+1)5…

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Q: az ) Use Implicit differentiation to find ax and for x2 – y2 +z? – 2z = 4 ду

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Q: Find y" by implicit differentiation. 3x3 + 4y3 = 2

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Q: Use implicit differentiation to find az/əx and az/ðy. x² + 4y2 + 5z2 = 4

A: Given

Q: Find the derivative of fG Cos' (3x²) 2. %3D

A: Consider the given function:…

Q: Use implicit differentiation to find zx x6y5-x4tan z + 2y2z3 = 7

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Q: What is the directional derivative of the function f(x.y)-2xy-3y at point p.- (5,5) in the direction…

A: To find: The directional derivative of the function f(x,y)=2xy-3y2 at point P=(5,5) in the direction…

Q: Use the derivative to find the critical point of f(x) = Ax² + Bx + C. Assume that A, B, and C are…

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Q: Find the derivative of the function. (3x +5) f(x) = In (7x + 5)*(2x+ 8) 14 2 O a. 3x +5 + 7x +5 2x…

A: We have to check

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan(x) 5t…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x (x+ 3)5 15) у - In 6х- 8 A)…

A: Given that:y=ln1-xx+35To find derivative

Q: Find the derivative of the function. h(x) = In[(2x + 8)(3x +6)] a. (2x + 8) (3x +6) 1 1 Ob. (2x + 8)…

A: The objective is to find the derivative of the function h(x) .

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x y = In (x + 2)5 4x - 7 (x +…

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Q: Q1 Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

A: as per our guidelines we are supposed to answer only the first question. Kindly repost other…

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: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the func - 2t dt g(x) =…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan x y =…

A: According to the Fundamental Theorem of Calculus, If gx=∫axftdt , then g'x=fx Consider the given…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan(x) y…

A: We have to find derivative

Q: f(x) = 2x² cos(r®)

A: Given Data: Function: f(x) = 2x2 cos(x5)   The product rule of differentiation is,

Q: Find the derivative of f(x) = v3x + 1 using the general formula for differentiation.

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Q: Find The derivaTive of f(X) = -x²+ 3X + 2 Using the de finiTion of the derivative

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Q: Find the derivative of by using the product rule. * (1+ væ³) (x-3 – 2a) y =

A: Consider the provided equation, y=1+x3x-3-2x3 Find the derivative of using the product rule. The…

Q: Find y" by implicit differentiation. 4x3 + 5y3 = 6 У" :

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Q: Find the derivative using the long method 3 u = t2

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Q: Find the second derivative (y”) of 4x2 + 9y2 = 36 by implicit differentiation. a. -16y3/9      b.…

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Q: Find the derivative using the definition fex)- = C fcx) fCx) = そり f ex) = KX" f cx) fx) = gx).hcx) 9…

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Q: Find y" by implicit differentiation. 5x3 + 4y3 = 9 У" - %3D

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Q: 23-4z2-2一4 y = %3D 1+ Va

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Q: Find y ' by implicit differentiation for 4x² y7 – 2x = x5 + 4y3 . %3D

A: We have to find y' by implicit differentiation of : 4x2y7 - 2x = x5 + 4y3

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: 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 the second derivative by implicit differentiation of 8x2 + 16y2 = 144 at (1, 1)  Choices: A.…

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

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Q: Find y' by direct differentiation (with respect to x). y = (5x2 + 6x − 7) ln x   and  y = (e-x)/…

A: Solution -a.)Given function -y = 5x2+6x-7lnxDifferentiating on both sides with respext to x,dydx =…

Q: Find the fourth derivative of f (z) = 27 + In (z) – 160z. %3D

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Q: If z = f(x,y) = 3x^2 - xy , get the total differentiation of z if (x,y) change from (2,3) to (2.5 ,…

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Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

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Q: Find the derivative of the function. 4x - 5 8x + 1 dx dx d (8x + 1) • (4x - 5)– (4x – 5) • d (8x+1)…

A: Explanation of the answer is as follows

Q: Use implicit differentiation to find az/əx and əz/ðy. x2 + 4y2 + 7z2 = 4 dz ax az

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Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. 3x + 4 y…

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Q: Find the maximum directional derivative of the function f(x.y) = x In y + x2y2 at the point (-1,1).…

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Q: Find y' by direct differentiation (with respect to x). y=-x2+2x5-e-6x

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the derivative. USING CHAIN RULE 4 y = V3x² – 5x + 2

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