Show that log, (Vx + Vx – 1) + log.(Vx – Vx – 1) = 0.

Q: Find dy/dx of the function. y=log2 x

A: To find derivative of given function.

Q: find f'(x) of (((3x^2+1)e^x^2)/(2x+1)^5)^5 using logaithmic differentiation.

A: The given function is,

Q: X* Q: Prove that the function y- 2 2 x+1+/log Vx+Jx +1 + log satisfies the relationship 2y=x dx

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Q: Find the second derivative of the following function: y = e** + = ex², +In(7e¯* + 5x³) – 52x 3x V

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Q: Q2) A: Compute 2 at the point (1, 0) for the function dx S(x.y) = cot(4x + eln(sinzxy)) + sinh(3) +…

A: Consider the given function. f(x,y)=cot-1(4x+ein(sin2xy))+sinh(3)+log2x2

Q: a) f(x) = x² is shifted to the right 5 units, horizontally compressed by a factor of 1 then 3…

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Q: Find the differential of each function: (a) y =(x' -3)* (b) y= V1-

A: Solution of this question is

Q: What is the derivative of e7 ** (4 x*+11)3 y = (16 x2+8 x-5)5 vith respect to x? Hint: Take the…

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Q: Find the indicated derivative or integral a. D, (3** * ) c. D, log,, (x³ +9) –3x а. D, b. |x 2* dx…

A: We know that Dx ax = ax·ln(a) Dx af(x) = af(x)·ln(a)·f'(x)   ∫ax dx = axln(a)+C   Dx loga x =…

Q: If g(x) = ªſ*'[e'− In(2t+1)]dt, find g ''(x) . - dx -2 4 A + (2x + 1)2 Be-In(2x+1) 2 C (2x + 1)² 4 D…

A: Given that,      gx=ddx∫-2xet-ln2t+1dt

Q: Find dy/dx of the following function using Chain Rule. y=(x3 + 3)5

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Q: 1 dx = +C (x+1)² X+1

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Q: Use the Power Rule to compute the derivative.

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Q: Evaluate the function: dx (x+1)–Vx+1

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Q: Q2) find the derivative of the functions : 10 logą t (3x²-1 1) y 2) f(x) = 2x+5

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Q: dy if y dx (22 – 3) /r³ + 4 x6 – 4x + 2 Using logarithmic differentiation, find -- NOTE: Eapress…

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Q: Find the logistic equation that passes through the given point.

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Q: Find the linearizationsof the following functions at x = 0. ex

A: fx=ex at x=0. Now differentiating with respect to x, we get f/x=dexdx=ex Now, f0=e0=1 & f/0=e0=1

Q: e* sin(3x° +4) dy find using the logarithmic differentiation. dx Given y Vx +2x

A: Please refer the attached image for complete solution.

Q: Use the Product Rule to compute the derivative: Find d/dt ((t^2+1)(t+9)) at t=5

A: To find  ddt[t2+1t+9]    at t = 5 Using Product Rule of Derivatives

Q: If F (x) = (t2) dt , then F' (4) = cos 0,

A: DUIS rule is used

Q: In(r) Find dy/dx using the method of logarithmic differentiation when y = (4+ 2x²).

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Q: where a = If loga z= dt, then r= exp

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Q: Find the derivative for the following functions: a)f(x) = log4 x + 6x² + J¤ 1 5 1 12x + f'(x) = x In…

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Q: dx 1-t+ x-tx dt

A: Given, dxdt=1-t+x-tx The equation is separable. Write it in differential form and integrate both…

Q: compute the derivative. g(t) = e4t−t2

A: The derivative of a function is given by the expression f'(x)=limh→0f(x+h)-f(x)h. For some standard…

Q: If e (3x + 2)e2* dy 3 4 using logarithmic differentiation. (b) show that +2 2.x-1 %3D (2x-1) dx 3x…

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Q: 4. y = log,(x* +3x² +1)

A: y = log(x4 +3x2 +1 ) here we use chain rule for differentiation dy/dx = (4x3 +6x )/(x4 +3x2 +1 )

Q: What is the derivative of (9x² + 14)2 (20x2 +11a- 15)3 123 e y = with respect to x? Hint: Take the…

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Q: Let y = (r-15x)m(). Find dy using the method of logarithmic d.x differentiation. Express your answer…

A: We will solve the problem

Q: Use logarithmic differentiation to find for the function dx (x3 +5) y = e2a /2x – 1 -

A: y=x3+5e2x2x-1taking log on both sidelogy=logx3+5e2x2x-1apply log…

Q: Find The Domain of the Function. y = sin(log, x²]

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Q: Find the differential of each function.  y = s/ (1+2s)

A: The given function is y=s1+2s To find the differential equation for function y, Since the given…

Q: Find the differential of the function  p = 5q − 6q3/2

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Q: find the differential of the following function u=2x^24+2

A: Given:

Q: dx = +C (x+1)² X+1

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Q: Find the differential of the function. u = 2x + 7 du = %3!

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Q: If f(t) is measured in dollars per year and t is measured in years, what are the units of f(t)dt?

A: We will find out the required unit.

Q: Find the derivative df/dt. * f (t) = 2' + In (t)

A: Given f(t)= 2t+lnt

Q: compute the derivative g(t) = e4t−t2

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Q: Use the Product Rule to compute the derivative: d Find dt (² + 1)(t + 9)) at t = 9

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Q: g(x) f(x) - sin(2²) dt, find f(x). = J

A: To Find: f'(x)

Q: Assume that all variables are the functions of t. If 3y2-2x2+4y=2x and dy/dt =4 when x-9 and y=12.…

A: Given,  3y2-2x2+4y = 2x   and dydt= 4  when x = 9  and y = 12  Then, we have to find the value dxdt…

Q: 4. y= log1,(x* +3x² +1) %3|

A: Given: y=log10x4+3x2+1   As we know that; The Power law; ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x…

Q: b. By using MatLab Find the second derivative of the function. f(P) = (In(P + D))VT– 2P7 eK+3P…

A: MATLAB code: syms p  %defining variable PK=2;D=1;%defining k and dfp =…

Q: Find the derivative of the function. V y= In 8v +5 dv

A: NOTE: Refresh your page if you can't see any equations. . take derivative apply chain rule  so…

Q: Give a physical interpretation of JT. F.ndS.

A: This expression is of surface integral for calculating the area of the field bounded in the…

Q: Let y = (x³ – 4x)(=) Find dy/dx using the method of logarithmic differentiation. Answer:

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Q: Find dy/dx of the following function using Chain Rule. y=(-3x5 +1)3

A: we use chain rule for differentiation y=(-3x5 +1)3 dy/dx =3(-3x5 +1)2(-15x4) dy/dx = -45x4(-3x5 +1)2…