e-2¤1 + 5x2x% 8. Let y(x1, x2, x3) = #3«3 – 20| and F (x1, #2, T3) = ( n - хо — 2.х1 + sin x3 - (a) Calculate y' and F'. (b) HENCE find (yF)'.

Q: --1/0 -1 -1 1,0

A: As we can see  in the figure the tangent line passes through the point x=2. Slope of tangent line…

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Q: (2x+3) 8. S- (x2 +x+2)2

A: Let's find.

Q: For the function f (x) = 5a- 7x +4r + 3 %3D a. Find f '(x) b. Find f" (x) c. Find f" (0) and f “ (2)…

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Q: Find *: (a) 4x°y³ + 2x³y-y-2x-4 0. %3D

A: Given  4x5y3 + 2x3y - y - 2x - 4 = 0 We have to find dydx.

Q: (d) dx (e) S,(4x + 2)5 + (6 – 4x) dx (f) S,' 4x3 – 3x* dx

A:

Q: f(x) = +x* – x' x² + 2x – 1 4 - - -

A: Given: fx=14x4-23x3-12x2+2x-1

Q: 2. Find f'(1) if f(x) = 3x³ (√x-2).

A:

Q: ((x/y)/z)+(x/(y/z))

A: In mathematics, precalculus is a set of course that includes algebra and trigonometry to prepare…

Q: Differentiate 3x-1 2x + 3 with respect to 'x'.

A:

Q: Find y" from x =t +7, y = 6t -1

A: Answer and explanation is given below

Q: f(x) = Ax , g(x) = Bx^2 Find A and B if (f o g) (1) = 11

A: This is a simple question based on composition of functions which could be solved with the basic…

Q: 3 find f'(x). x2 7 If f(x) = 7+ -+

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Q: Find the derivative of the function g(x) = g'(x)= = e² 4 - 2x

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Q: f(x) = C

A: Here we apply quotient rule of differentiation given as ddxuv =vdudx-udvdxv²

Q: Evaluate the function when x = 1, 3 and 3 3 1) f(x) = x + 2x - 3

A:

Q: Find f such that f'(x)=6x-5, f(6)=0. f(x) =

A: Just i have integrate the given function and then use the given initial condition and then find the…

Q: 2x+5 dx = AV7- 6x - x2 + B sin - (**)- 1. Vア-6xーx2 +C

A: ∫2x+57-6x-x2

Q: (x? + 3x — 45)dх J«+ 3)(х + 12)(4х — 3)

A:

Q: 4x - 7x Differentiate with respect to 'x' 6x + 5

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Q: Let f(x)= ax'+x² + bx +6 where a and b are real numbers, and f(2)=3. Find the value of f(-2).

A: f(-2) = 17  The detailed solution is as follows below:

Q: The derivative of f(z) - (+10z) is O6z (2z + 10) O6z (2z+10) O 6z (2z + 10) O 6z+60

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Q: Evaluate (*(x-2) (х-1)3

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Q: Simplify the expression xyz + x’y + x’y’

A: We have to simplify the expression xyz+x'y+x'y'.

Q: Q2-Prove that

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Q: r³ (x + 2) 6. Find f'(6) for f(x) = V (x + 3) Væ2 – 27 11 (a) 18 11 (b) 216 11

A: Some common derivative rules are, Also,

Q: (х, у) — ху? + yex- +5

A: we have to find fxx and fyy.

Q: 7- Differentiate Y= f(g(x4)) h³(√x)

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Q: る(4xナx)(10x2+x2-2

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Q: x3 – 3x2 – 6x - Show that - = x-3 - x2 – 9 x – 3'x +3* - - x3 - 3x2 - 6x -dxp. Hence, evaluate x2 -…

A: To show: The equation x3-3x2-6xx2-9=x-3-3x-3+6x+3 and then evaluate the integral ∫x3-3x2-6xx2-9.…

Q: Let y = xbex (where b is a real number). Determine y'.   Let y = (3x + 6)/(6x + 12). Determine y'.

A: given y=xbex to find the derivative y' use the product rule uv'=uv'+vu' therefore,…

Q: 140 士+0 9 -1 -1 cBook Pro * 1)

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Q: f"(2) 1. Find

A: Given f(x)=43x2-23x+1f'(x)=-23*ddx(x)+43*ddx1x2+ddx(1)        =-2*13+4(-2)x-33+0

Q: dx J x²–18x+97 O fIn (x² – 18x + 97) + C In (x² – 18x + 97) + C 0sin-l (부) + C х-9 O tan-' () + C…

A:

Q: 3. -2x-4 dx x-3 6x 4. (x2-7):/

A: (3).   The given integral is: ∫x3-2x2-4x-3dx

Q: If f(x)=√√√x² - 4x + 19, then what is f'(1) ?

A: Given query is to find the indicated derivative.

Q: 2. In the following function, determine f'(x): 2 a. 3√√x2 b. 15x4 C. 1 2 x² +6 x3 20x320 2

A: NOTE: As per the guidelines, I have solved three parts. If  you want solution of the remaining part,…