Find an equation of the tangent line at the point specified. y = 4 sin(x) + 6 cos(x), x = 0 4x + 6 OTutorial The equation of the tangent line of f(x) at x = a is y = f'(a)(x - a) + f(a). Hov Additional Materials eBook

Q: a. 1 y" + 2y' + y = -e™* b. x²y" + xy' + 4y = sin(2 ln x),x > 0

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Q: Hi, I need help with solving these derivatives. Thank you for your help! g(z) = 2z" – ež In(z) -…

A: The given functions are: gz=2z7-ezlnz f(t)=lne4t+3+cos3tg(x)=12x·x2+1

Q: IV. Implicit Differentiation. Determine the derivative dy/dx of the following equations. 14. x +…

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Q: ACTIVITY 2: Find the derivative and simplify the result, if possible y = x2 + n² +x" y = x2 sec x y…

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Q: 2. (a) This is correct. (b) This is correct. (c) This is incorrect. Because the differentiation is…

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Q: Find the equations of the tangent line and normal lines to the graph of the function f(x)= —4 sinx…

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Q: B. Derivatives of Trigonometric Functions dy Using the formula find dx 5. у-сos (2x-1)

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Q: = 1. Let y? + y = x. Using implicit Suppose that y(x) is a function and that y(2) differentian find…

A: Given  y2+y=x y2=1 To find : y'2 and equation of tangent to y(x) at x=2.

Q: 45-56. Repeated use of the Chain Rule Calculate the derivative of the following functions. 48. y =…

A: According to bartleby policy ...I have authorised to answer 1st one question.....for rest…

Q: F f(z) = -3e sinr, the second derivative f"(x) is: %3D

A: Given f(x)=-3ex·sinx Taking first derivative with respect to x, we get f'(x)=-3ddx(ex·sinx)…

Q: у 3 sin (x? + 3x + 1) 1. 2. у%3D сos?(2х — 1) y = tan vx2 – 1 3.

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Q: Db taln the wafun 2 couu) sec'x dx + tanx

A: According to our guidelines I can solve only one question at a time if you want solution of other…

Q: 2 sin x Let f(x) : 4 sin x + 2 cos x Then f'(x) = The equation of the tangent line to y = f(x) at a…

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Q: 1. x sin y-y cos x = C

A: Topic - differential equations

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Q: a3 f 2- Find the third derivative for for f (x, y) = sin əx3 -2sin?cos()+2 sin) sin By'sini )+2…

A: The given function isf(x, y)=sinxy

Q: 7. у%3D Arccos(eе*)

A: y = Arccos(e^(2x)) double derivation y''.

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Q: 2x ind the derivative of: 2e cos(8x). [Hint: use product rule and chain rule!] se e^x for e*. ow,…

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A: Given function is : gt=sint To find the slope of tangent line at t=-π6

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Q: 2x y= Arccos(e)

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Q: (a) Find the second derivative of the function y = 2x sin(x). (b) Find the derivative of the…

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Q: 6. In(x®y²) = x² +y³

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Q: tan (sinh x) ) ds (b) cosh a sinh x sinh

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Q: ELIMINATION OF ARBITRARY CONSTANTS 1. y = x² + Ae2x + Be3x 2. y = C1e*cosx + C2e*sinx %3D

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Q: et +e» et Рe-* cosh(x) sinh(x) 2

A: Given that:- coshx=ex+e-x2 sinh(x)=ex-e-x2

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A: Topic:- Differentiation

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Q: IV. ELIMINATION OF ARBITRARY CONSTANTS y = C,e*cosx + Cze*sinx

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A: Given,

Q: . (sin a+ cos x) dy + cos x- sin x) de = 0. (Ans. y + log | sin x+ cos x|c)

A: Formulae used: ddxsinx=cosxddxcosx=-sinx∫1dx=x+c∫1xdx=log|x|+c

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.