Evaluate F. dr where F = (0, -3y, 3x), and C' is given by F(t) = (t, sin(t), cos(t)), 0

Q: of of and dy 6. For the function f(x.y) = sin ° (6x - 5y), find of df dy II

A: In partial derivative when take the derivative with respect to one variable consider other variables…

Q: Find f if ƒ"(t) = 2et + 3 sin(t), ƒ(0) = 2, ƒ(π) = 5. f(t) =

A: f''( t ) = 2et + 3sint f( 0 ) = 2 f( π ) = 5

Q: Find the local extrema of the function f(x, y) = e-(cos(r)+sin(y)) and test for which are max, min,…

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Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

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Q: 4 (t) = -5 sin t + 8sec?t – 8 csct cot t + 4et + - 1+

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Q: f (x) = 3 sin x + 3 cos x, [0, 27]

A: Consider the function: fx=3sinx+3cosx Differentiate the given function with respect to “x” then,…

Q: 2. Find the derivative (dy/dx) of the following functions: n) y = 1- cos 3x sin 2x + sin 8x tan 4x

A: 2) n) It is required to find the derivative of the function y=1-cos3xsin2x+sin8xtan4x.

Q: sec? r da = F(x)

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Q: Find F as a function of x and evaluate it at x = 0, x = /3, and x = = Tt/2. F(x) 6 de

A: We will use basic formula of Integration for first one and from second part just Value of the…

Q: 2. Differentiate. f(t) = et sin(2t)

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Q: Find the derivatives of the functions

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Q: Let f(x) = – 3 sin( – 2x – 5) – 6?

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Q: Differentiate the function. P'(W) = P(w) = 6w² - 4w+2 √w W

A: To differentiate the following function.