Use the Chain Rule to find az/əs and âz/ât. z = x²y⁹, x = 5 cos(t), y = s sin(t дz əs əz at || [(C+())[- ² - 3] (주) | 2 e S e S 2 X X

Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: Let f(æ) = sin(x) and g(æ) = x² . Find (go f)'(x) O 2sin(x)cos(x) O 2xcos(x?) -2æcos(x?) 2xcos(x)

A: Given that f(x)= sinx and g(x)=x2. And we find (g0f)'(x). We know that d(xn)/dx = nxn-1.     Here i…

Q: Compute fx cos xe dx by using substitution. sin.x²

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Q: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

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Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

Q: find ap for f(x) =cos 2 [0,2n]

A: a0=0

Q: What is the coefficient of x2y' in (5x- y)?

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Q: h(t) = / e -3(t-T) cos(27)dr. This is the convolution of two functions f(t) and Consider g(t). That…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Determine whether the given set of functions is linearly independent on the interval (-co, co).…

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Q: x3 C. g(x) : et

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Q: Find y as a function of t if 4y" +12y +9y = 0, y(0) = 6, y(0) = 6. 42 y(t) = 6 cos(-¹)+sin(-)

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Q: Hence, using chain rules find y' i. y = sin(2x² + tan(6x² – x)),hint: u = 2x² + tan(6x² – x) ii.y =…

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Q: Let f(x, y) = 2x - 5y, r(1) = (cos(t), sin(t)). Use the Chain Rule to calculate f (r(t)) at the…

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Q: A) Find the first and second derivatives of the function g(x) = Vx² + 2x .

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

Q: Find r'(t), r"(t), and r'(t) • r"(t). r(t) = 7 cos(t)i + 9 sin(t)j

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Q: (a) a²y + y sin r = xy. (b) y = x³y - 2y³. (c) y = e²-2y (d) y'= x² + y² xy

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Q: I. Find y', y" and y"" of the following functions. a. y = 2x-x'+ 5 b. y = (r²+2) x-1 II. Use the…

A: I. (a).y=2x4-x3+5diff w.r.t xdydx=2(4x3)-3x2+0y'=8x3-3x2diff w.r.t x…

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

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Q: U tt = quna %3D u(x, o) = Cos(x) Ut (X, o) = los (2x) %3D

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Q: Are fi (x) = x, f2(x) = x², and f3(x) = 4x – 8x2 linearly independent or linearly dependent on (-00,…

A: Definition: A set of vectors are said to be linearly independent, if no vector can be represented as…

Q: f(t) = -3+4 cos(,(t – 3 ).

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Q: find the derivatives complex funcation. {tanh¬'(iz +2)}-1,

A: fz=tanh-1iz+2-1=1tanh-1iz+2 It is known that tanh-1x=11-x2 so it follows:…

Q: If f(x, y)= cos(x +y), then- (+: O a. - sin (x + y) O b. - cos(x+ y) COS O c. cos(x+ y) O d. sin (x…

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Q: -4 (b) If u find and expressing all derivatives in their simplest 3xy form. Hence, Show that

A: The solution is given as