If f(x,y,z) = 2x² − yz + xz², where x = 2 sint, y = t² − t + 1, and z = e−³t, find f't)

Q: Find y' at the point (6, 6) where x sin(x? – y²) + 33 = x? – 3.

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Q: (1-x) y'= y?

A: We have to solve the given differential equation

Q: Let f(x) 6 sin x + 4 cos z Then f'(x) = The equation of the tangent line to y = f(x) at a = π/3 can…

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Q: Find the derivative of g u g(x) (2)=√1² +38 du u 5

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Q: 3 Find f'(x)given f(x) = x/x – 4x – 7x %3D

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Q: Find f(x), where f'(x) = sin(x)+ cos(x) + 1 and f(r) = 2. %3D %3D

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Q: Find f'(z) of f(z) = 3πi.

A: Compare the given function f(z) = 3πi. with f(z)=u(x,y)+i v(x,y) So,  u(x,y) =0 and v(x,y) = 3π

Q: Suppose y is a function of x. Find y' given csc-1y + xy = sec 1 y.

A: Given, csc-1y+xy=sec-1y

Q: Find f if f'(x) = sin x + cos x, f'(0) = 7, and f(0) = 7. Answer: f (x) =

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Q: sinx If Ax) = 2**, find f'(0). A 2 cln2 D1

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Q: 5sin x d) y = In 2

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Q: Q2/ if y = Jsec3 /sin+Vx+ x² 4. find y'

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Q: Find f. f ''(t) = 4et + 6 sin t,    f(0) = 0,    f(?) = 0

A: To find f. f''(t)=4et+6sint,f(0)=0,f'(0)=0

Q: d csc 'x dx -1 Prove that xVx? – 1 2.

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Q: Let F(x) = sin 3t dt, please find F'(0)

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Q: Use the rule for square roots: f'(x) 2/ F(x) V F(x) to find the following derivatives (quickly d V…

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Q: cosh r – 1 · (xª4 + 2) +2). Compute the derivative of y = In | (2x + 1)

A: Given problem:-

Q: Find f if f"(t) = 2e¹ + 3 sin(t), f(0) = −4, ƒ(ñ) = 9. f(t) = 2e^t-3sint-6

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Q: Apply the 1t derivative property to : 1) f(t) = e-2tsin5t 2) f(t) = = cost sint 3) f(t) = e²tsin2t…

A: Solution

Q: If f(w) (3w), find f'(w). Use exact values. = COS f'(w) =

A: We can find the exact answer as below.

Q: dy of the function dx Find the derivative x² In 3y = y sin 3x + e2a.

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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 f. f(x) = f"(x) = 5ex - 7 sin(x), f(0) = 3, ( 77 ) = 0 EN 2

A: Given :f''x=5ex-7sinx