Use the Chain Rule to evaluate the partial derivative y = 3r sin(0). (Use symbolic notation and fractions where needed.) dg 20 (r,0) = dg at the point (r, 0) = (2√2,4), where g(x, y) = x + x² > , x = 8r cos(0),

Q: 2x -1 If y-f and .1 + 'א. dy f'(x) - sinx".find - dx

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Q: (5) (sec-i x) =, d

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Q: Find the derivative of y = (4 - 2x³)(2x + x³). O a. y= 12x5+ 16x - 12x² - 8 O b. y = 12x° + 16x³ +…

A: As per our guidelines we are supposed to solve only one question i.e. the first one. For the…

Q: y=(4x -5x +6)(e-sin 2x), then find dy at x 0.

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Q: Q2) Use the chain rule to express dy /dx in terms of x and y y = sint and t = cos x where t= 0

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Q: [4] S (x + )´ dx [5] S cos²(2x)dx X. V1+x3 [6] S- dx r-2

A: To evaluate the integration of the following.

Q: Identify the function f (x). I (x) = (f (x))° = cos 2x

A: Given,          lx=fx6=cos62x

Q: Calculate the derivative using implicit differentiation: சம dz || -2zw - 7y (x³ +8w+z²) θω dz…

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Q: Q3: Use Chain Rule to differentiate the following functions 1. f(r) = (4x² - 3r + 2) 2 2. y = csc(4…

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Q: Given: g(x,y) = (x2 + y - 11)2 + (x + y2 - 7)2 Find (1) the derivative with respect to x and (2)…

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Q: Jx + 2x f(x)=- 7х — 4х? 8.

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Q: Which of the following functions satisfy x²dy+ y(x + y)dx=0 with y(1) = 1 ? 3x²y = x+y 3x²y = 2x-y…

A: Given the differential equation: x2dy+yx+ydx=0 with y1=1 To find out which function satisfies the…

Q: 15. 17. f(x) = (2x – 3)*(x² + x + 1)* - 18 19. AU

A: From the derivative of given function

Q: Q3) Find the approximate root of the following equation f (x)= cos x – x e* = 0 , on the interval…

A: The given equation fx=cosx - xex=0 on the interval 0.25,0.75 Use the bisection method…

Q: f(x + Ax) - f(x) D. APPROXIMATE DERIVATIVES f (x) Ax 7.) y = x2 +7x – 10

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Q: 2+ cosh r (r² + 4) Compute the derivative of y = In I - (r+ 1) Compute the derivative of f(x) =…

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Q: Express the indicated derivative in terms of F(x). Assume that F is differentiable. (9 + (F(5x)))³ d…

A: It is known that , if we have a function f(ax) then the derivative of the function will be defined…

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t and x = sec-1t

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Q: f(x.y) = xtan(). =tan( ес

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Q: Find derivatives of: 1.) f(t)= 7t          2.) g(x)= 3x-9      3.) h(v)= v3 4.) m(x)= π2

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Q: Which of the following functions satisfy x²dy+ y(x + y)dx = 0 with y(1) = 1 ?

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Q: Let f (x) = 2 tan (5x). Find the values of the coefficients in the expressions for f'(x) and f " (x)…

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Q: Use the rule for recipocals : f '(x) f?(x) d 1 dx [ f(x) to find the following derivatives…

A: Given: Reciprocal Rule: ddx1f(x)=−f'(x)f2(x) Find: 1)  ddx1x2+2x+1=?2)  ddx1sinx+ex=?3)  ddxπx+1=?

Q: Find y as a function of tif y(3) = 8, y'(3) — 9. Y - 49y"+126y + 85y = 0,

A: Find  as a function of  if  ,  .