If ƒ(x) = sin(e²x), find ƒ'(x). ƒ'(x) = ←

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A: Given

Q: Find the linearization L(x) of the function at a. f(x) =  3   x,    a = 64

A: Find linearization L(x) of the function at a. f(x)=3x , a=64

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Q: 21. sin(x + y) = x + cos 23. xe" = 2xy+y3

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Q: please show full calculations

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Q: SH E

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A: Please see the below picture for detailed solution.

Q: 6. Suppose we don't know the formula for the function y = f(x), but we know that f(2)=-3 and that x²…

A: Given: f'(x) =  x2 / ( √1+x2 ) f(2) = -3

Q: Use L'Hospital's rule to determine the following limit. Use exact values. 9ª - 82 lim x-0 x

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Q: Find the general solution of the given differential equation. x²y + x(x + 2)y = ex y(x) = Give the…

A: To find the general solution of the  given differential equation. x2y'+xx+2y=ex To  give the largest…

Q: If f(z) = æ®sinh`1(6x) then f'(x) =

A: f(x)=x3sinh-1(6x)d dx(xn)=nxn-1d dx(sinh-1x)=11+x2d dx(a.b)=adbdx+bdadx

Q: -0.5 0-1.0 6 X co 10 12 -0.5 O-1.0 (h) When, for 0 ≤ t <∞, is the particle speeding up? (Enter your…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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A: this is question of calculus  here we have to find function  further calculation is given below

Q: Find the differential of the function w=x^2sin⁡(y^2z^5) dw=dx+ dy+ dz

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Q: Find the solution of with y(0) = 8 and y' (0) = 1. y = y" + 2y + y = 16 e¹t

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Q: Determine whether the sequences are increasing, decreasing, or not monotonic. If increasing, enter I…

A: As per guidelines, we can solve only 3 subparts. Please repost the other parts and mentioned the…

Q: In Exercises 9-26, calculate the derivative with respect to x. 10. y4 – 2y = 4x³ 12. xy² +x²y5 – x³…

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Q: Consider the following. f(x, y) = x + y ya 0 (1, 1) D (a) Express the double integral 2 x JS f(x, y)…

A: Consider the following. fx, y=x+y (a) To express the double integral ∫∫D fx, y dA as an iterated…

Q: If a bomber flying at 34125ft at 540 mph wants to bomb a target on the ground, when should the bomb…

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Q: Choose the expression equal to (Use implicit differentiation.) E dx In(x + y) = x

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Q: Find all the local maxima, local minima, and saddle points of the function. 3 3 f(x,y)=x² - 6xy + y

A: To find the local maxima, local minima, and saddle points of the given function, we need to find its…

Q: y = 2x² - 8x. Determine the slope of the tangent to the function at x = 2.

A: To find the derivative of the function y=2x2-8xusing first principles,we start by using the…

Q: Consider the series (See image). a. The general formula for the sum of the first n terms is Sn =…

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Q: Find fx and fy, and evaluate each at the given point. xy (9,-9) x-y f(x, y) fx(x, y) = fy(x, y) =…

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Q: Find the derivative of y = sin¹³(t). dy dt I

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Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 15 m/s, its height…

A: If h(t) is the height function then h'(t) is the velocity function.

Q: Find the cross product a x b. a = ti + cos(t)j + sin(t)k, b = i sin(t)j + cos(t)k Verify that it is…

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Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) (x² + x 5 3 ) lim…

A: Topic = Limits

Q: Calculate, to four decimal places, the first ten terms of the sequence. - (-³/-)" an = 1 + n 1 2 3 4…

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Q: An angler hooks a trout and reels in his line at 3 in./s. Assume the tip of the fishing rod is 13 ft…

A: first define terminology hypotaneous = zperpendicular = yhorizontal distance = x

Q: In constructing an open rectangular box from 147 ft of material, what dimensions will result in a…

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Q: dy Choose the expression equal to dx (Use implicit differentiation.) if tan(x + y) = X

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Q: Find the linear approximation L(x, y) of the function f(x, y) = 3x² – 2y² at (1,1). A. L(x, y) = 6x…

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Q: If z = ln(2x+y), x = u sin v, y = v cos u, find az/av when u = 0, v = 1. A. -2 B. -1 C. 0 D. 1 E. 2

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Q: The number of thousand mp3 players produced per month by a certain manufacturer t months after the…

A: Given :- The number of thousand mp3 players produced per month by a certain manufacturer t months…

Q: Chris Lynch plans to invest $400 into a money market account. Find the interest rate that is needed…

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Q: The census bureau for a large country has reported that the country is becoming more diverse. The…

A: Given : The projected populations of a certain minority is modeled by exponential function…

Q: Solve the equation. (2x³ + xy)dx + (x³y³ -x²)dy=0 An implicit solution in the form F(x,y)=C is =C,…

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Q: B- Find the equation of the tangent line to the curve y = x² - 2x at x = 3

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Q: 19. r(t) =(√2t, e', e-¹')

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Q: S COS X sin x+sin³ x dx. (b) ſ sec²x tan x+4tan³ x dx.

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Q: Related Rates: Suppose x (t) and y(t) are differentiable functions satisfying x³y - 3x√y + 2x = 0…

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Q: Use the relevant information to compute the derivative of h(x) = f(g(x)) at x =1, where f(1) = -3,…

A: Given that, h(x)=fgx

Q: 5. fx³ cosh¯¹(x²) dx

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Q: Write an equation for the function graphed below -7 -6 -5 y = -3 -2 -1 5 in P P 7327? -4 -5 5 6

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Q: Find the derivative of f(x) = (2x-4)(3x+6) x-1

A: The function is given by fx = 2x-43x+6x-1 To evaluate: The derivative of the function. Formulas…

Q: хе f ex: z =_ху 4х2+4у2 Odz () (4x2++y)-04-2 8X сах2+чучук ze he L f'.g-f.g' органда 4x2+4y3

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