A-1 In At1 dy e4z+1 Find dx of the function by logarithmic differentiation y a.

Q: dy 7. Find by implicit differentiation. dx 8. Use logarithmic differentiation to find y'. 4x4y6 = y…

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Q: A local pond can only hold up to 51 geese. Seven geese are introduced into the pond. Assume that the…

A: This is a problem related to differential equation and exponential function. Based on the general…

Q: 1 What is the instantaneous rate of change of Y= at x = 2? - o-1 4 O none of these -1 -1

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Q: Q.NO.3: dy i. Find using logarithm differentiation dx 5 x - 1 x + 1 ii. Find a point on the curve y…

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Q: 19. The function ƒ(x) = ex + x, being differentiable and one-to-one,has a differentiable inverse…

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Q: / Find dy/dx for the followings functions: 1) y = x(x+1)(x-2) (x+1)(2x+3) use logarithmic…

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Q: b). Using gamma function, evaluate S x® e-2* dx c). Shrinks have discovered that there is a limit to…

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Q: Q1/ Find dy/dx for the followings functions: 3 x(x+1)(x-2) 1) y = use logarithmic differentiation…

A: From the given problem:   y=xx+1x-2x2+12x+33   Now we can simply write as:   y=xx+1x-2x2+12x+313…

Q: How do you solve questions 1 and 2?

A: Logarithmic differentiation – When there is x or a function of x is in the exponent of any number or…

Q: (x +1)(x+3)2 is given, find derivative of y. x-1 (hint:you can use logartihm) , x²+1 x+3 x- 2x k dy…

A: The detailed solution of the problem is given in the next step.

Q: a) f'(t) if f(t) = e2sin t – In(t³ + 1) + ve b) if y=x (Use logarithmic differentiation) d) if x-…

A: We have to find the derivatives.

Q: y²-9 a:Sketch the function x = log_0.5 b:If y = e-2x+1 e-2х-1 d²y prove that, dx2 dy 1- 2y dx

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Q: Question number 8

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Q: You want to differentiate Y = E coe) so you take the the natural log of both sides, first. What is…

A: Consider the function y=lny.

Q: (a) Find the derivative. y In(4x – 5) – 3 In(x) dy dx (b) Find the derivative. 4x - 5 y = In x3 dy…

A: a) First we shall find the derivative of y=ln4x-5-3lnx Now,…

Q: 6) Consider the exponential function f (x) = ex* [C:4] a) Determine the n-th derivative of f(x). b)…

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Q: Consider the chemical reaction model described below. dy ky? dt Rate of change of y is própor-…

A: According to question given that dydt=ky2We have to calculate for yy=60 grams, when  t=0y=18 grams,…

Q: I+1 Evaluate f -dx (T+2)(x+3) 2 · In\æ + 3| – In|x + 2| + C 21 I+3 I+2 2 · log10 ¤ + 3| + log10|¤…

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Q: nt A model for the basal metabolism rate, in kcal/h, of a young man is R(t) = 70 - 0.16 cos where t…

A: Given: Rt=70-0.16cosπt12 To determine: The total basal metabolism of this man.

Q: II. Find dy dx 2. y = Do not simplify your answers. tan ¹(cosh x) (sin²x) (sech x)sec a [use…

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Q: Example: Find y de (a) ey sin x = x + xy (b) y = x² sin¬1 (3x² 1) %3D - (c) y = x² (Hint: Use…

A: Differentiate above function with respect to x

Q: Q. No. 2: (a) Use logarithmic differentiation to find the first derivative of the given function.(3)…

A: Differential calculus is one of two main parts of calculus which is concerned with the study of…

Q: Jse logarithmic differentiation 14) = ル r+1 y%3D Vx2-4

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Q: Example: Find dy de (a) ey sin x = x + xy (b) y = x² sin¬'(3x² – 1) (c) y = x* (Hint: Use…

A: Using product rule of Derivative

Q: y=24x dy/dx=_____? 2. Find the derivative of the following function. A=860(1.610)t A'=_____?…

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Q: dy -3 sec" sing logarithmic differentiation, find given that y = dr (4*)(log, 1)sech z

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Q: Definite integrals Evaluate the following definite integrals. Use Theorem 7.7 to express your answer…

A: Given integral is ∫535dxx2-9 . Consider x = 3 sec u.

Q: Use logarithmic differentiation te find the dexivative of « with respect to the given independent…

A: In the question it is asked to calculate the differentiation of y=x(x-2)x2+13. It is also asked to…

Q: Using logarithmic differentiation, Show that y (x) = xa2"e*ħas stationary points other than a = Oif…

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Q: The capitalized cost C of an asset is given by C = Co + c(t)e¬rt dt where C, is the original…

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Q: f(x) = log(x)+In(x) %3D 22 - find the derivative value of f(x) at x=1. f'(1) = ? O A) 2+log(e) OB)…

A: f(x)= log (x) + ln(x) We need to find f'(1)

Q: Va +1(x+5) If y= show that dyVx +1(**5) i (x+1) 3 (b) by using (x+1) x² +1 x+5 dx logarithmic…

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Q: LUI (a) - f(x) = log(5 · xº + 7) − log(12) — 6 - f(1) = (c) line is (b) the curve y = f(x) at x = 1…

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Q: Example: Find de dy (a) eª sin x = x + xy (b) y = x² sin-1 (3x² – 1) (c) y = x* (Hint: Use…

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Q: Given the function y = f(x) = ln (x2" (arctan x)ot) %3D a) Use the properties of logarithms to…

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Q: Consider the chemical reaction model described below. dy = ky² dt %3! Rate of change of y is propor-…

A: Proceed as shown below...

Q: 6. The derivative of f(r) = a" + log, r equals %3D 1. 1 (a) f'(x) = In a · a" + In a r (b) f'(x) =…

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Q: 3x-2 dy Find dx of the function by logarithmic differentiation y zー24 O a. y- 2x'3r-2 6z-12 O b. y…

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Q: Find the derivative of the logarithmic function. y = In 6 + e 6- e*. Step 1 The given function y =…

A: We will derivate the function step wise as asked in the question.

Q: dy dx Using logarithmic differentiation, find NOTE: Express your answer in terms of x only. dy dx =…

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Q: An accident at a nuclear power plant has left the surrounding area polluted with radioactive…

A: The given scenario can be modelled by the equations dAdt=k At and At=A0ekt. a) The initial amount of…

Q: QI/ Find dy/dx for the followings functions: 3 1(x+1)(x-2) (+1)(2x+3) 1) y = use logarithmic…

A: Since you've asked multiple questions, as per the answering guidelines we are supposed to answer…

Q: The capitalized cost C of an asset is given by C = Co + c(t)e¬rt dt where C, is the original…

A: Sure. Happy to help.

Q: 3. Use logarithmic differentiation to find the derivative of the functions. (a) y = (r² + 2)*(x“ +…

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Q: The function ƒ(x) = e^x + x, being differentiable and one-to-one, has a differentiable inverse ƒ…

A: Given

Q: A tank contains 240 liters of fluid in which 30 grams of salt is dissolved. Pure water is then…

A: We have to find the rate at which the number of grams of salt in the tank is changing at time t and…

Q: 1. Use logarithmic differentiation to find the derivative of y=(sinx)^cosx   2. A particle is moving…

A: Given that : y = (sinx)^cosx.  Find logrithmic differentiation to find the  derivative. Here i…

Q: Calculate the active and reactive components of current in each phase of a star - connected 10,000…

A: Calculate the active and reactive current components in each phase of a star-connected 10,000 volts,…

Q: ind the tangent to the föliüm of t what points on the curve of x' +y 6xy is the tangent line…

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Q: A culture initially has Po number of bacteria. At t = 2hour the number of bacteria is measured to be…

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