By using first fundamental theorem of calculus. Solve the problem 1.) Suppose f(x, y) = S*3 If fx (0.=) = 2.find a dt e(x²+5x) sin y 8+cos*(2nt)

Q: 1. Find the derivative 4 ln 2) ³ 3x³ sin(2x) 5x2+3

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Q: Evaluate f x'V 1+4x² dx.

A: Consider the definite integral ∫01x21+4x2 dx to evaluate this, first evaluate the indefinite…

Q: this is a calculus problem find the dy/dx by implicit differentiation Square root over xy=x7y+58

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Q: Q3: A) Find the derivative for the following functions: 1) y = log(x Sinx) 2) y = tan(x') 3) y = (x…

A: The derivatives of the functions:   3) y=xsinx+2 taking logarithms both sides, log y=log xsinx+2log…

Q: If 7'(t) = (cos t, e2t, 3t²) and r(0) = (3, 1, –2), find the function 7 (t).

A: Given. f'(t) = (cos t , e2t , 3t² ) To calculate the vector function are we need to integrate the…

Q: If f (x, y) = x(x² + y²)-3/2 esin(a²y) find fa(1,0).

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Q: Let y -2 = S sin³ (t) dt. Use the Fundamental Theorem of Calculus to find y'. ex

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Q: Find L {f(t)} if f(t) = cos 5t + sin 2t

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Q: Find the derivative y = √√x S 3t cos (16) dt 0 A. 3 cos (x³) -3√√x sin (x³) OB. 3√√x cos (x³) OC.…

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Q: dy x3 + 2xy. y 7. Find for the implicitly defined function dx

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Q: If tan2(2y) – S cost dt = 4 - x² %3D dx

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Q: Given the function g(x) = :/ V4 + sin(31) dt, 2x3 use the Fundamental Theorem of Calculus Part 1 to…

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Q: 6. Find the derivatives of the following: a) g(r) = sin(vi) dt %3D g(=) = /" Ve +4 dt

A: Please refer to the image below

Q: 3) Suppose 2X z = xe cos 3y, find all the first and all the second derivatives.

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Q: 1. Find dx dy for the following functions: 1) y = (x- 3)(1- x) (ans.:4 - 2x) b (ans. :-,) x* 2) y=…

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Q: 1. Use the basic differential properties shown in section 3-5 to find each indicated derivative. (A)…

A: According to our guidelines, we can answer only three subparts of a question. Other parts can be…

Q: Q1) Use implicit differentiation to find dy/dx if a) (3xy + 6)2 = 7y b) x cos(3x + 2y) = y sin x %3D

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Q: (b) x = dx dt 1 sin7 (t³)

A: Given:- x=1sin7t3

Q: 4. Find the derivative of the following functions: a. y = x² sin x b. y = ex cos x 3 c. y = (x² + 1)…

A: *Note – As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly…