Show that log, (x + Vx² – 1) + log,(x – Vx – 1) = 0.

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: At what time does f (t) attain its largest value?

A: Consider f(t) is any function. We know that function attains its largest or smallest value when the…

Q: Find the derivative of the composite natural exponential functions 1. f(x) = In( 2. g(x) = In(v³ +1)…

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Q: Suppose that f(x) = 11x – 4 ln(x), x > 0.

A: (g) Find the double derivative for f(x).…

Q: . Use logarithmic differentiation to find y'(0) if y = Vcos3 r V5+

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Q: Find the MacLaurin polynomial of degree 7 for the function sin (ot) dt. F(X) = %3D

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Q: 1 dx = +C (x+1)² X+1

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Q: Find the equation of the secant line for f(x) = log2 (3x² + 2x – 1) from x = 1 to x = 3.

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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: 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: 5. Use the chain rule to find the derivatives of (a) y = log; V4 + 1 (b) y = (x – e-")²

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Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

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Q: 23: Find The Domain of the Function. y = sin (log, x²]

A: Given: y=sin-1[log4x2]

Q: Differentiate the following using chain rule Y = In (cot 3x – 2) Y = log cos? 3x

A: We need to find the derivative of Y=ln cot 3x-2 and Y=log cos23x. First problem: Now,…

Q: Let f (x) = e10x. %3D Find a formula for the n-th derivative of f, for n 2 1.

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Q: Find the derivative of the following function f(z) = log, (5 +2*) %3D 57 + 5z4 (5 +5) In (2) O 5 In…

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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 first derivative: b) y = log7 v1+x

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Q: Let f(x)= [(x+4)^5(4x-1)/(6x+3)^5]^1/6 Use logarithmic differentiation to find the derivative of f.…

A: The given function is

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: f. y=In(x8+1)

A: We will solve the problem

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: Find the derivative of the function. y= log , (3x2 - 2x) 5/2 O A. In 9(3x- 1) (3x2 - 2х) OB. 10(3x –…

A: We need to apply 1.chain rule 2.differentiation of logarithmic   we get option c as correct answer

Q: Find the derivative of the function. g(x) = In| 8x – 9 | a. 8x -9 Ob. Sx -9 O. none of these 1 Od. -…

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Q: Exercise 9. Use properties of logarithms to find the derivative of S(2) = In (3z – 2)(v/=" + 1))…

A: From the given problem;   fx=ln3x-2x3+1   From the property of the log.   lna·b=lna+lnb   So, we can…

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: 7. Find the derivative of each funcrion. a. y = 5-4* b. fCx) = xqx d. FCx) = Togax-1 C. Y =…

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Q: Determine dydx of function g 1 g(x, y) = cos (Tx/T) + log3 (x – y) |

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Q: Find the derivative, dy/dx: y = log3 (2x +1) Oy =- (2z+1)3 In 3 Oy = (2r+1) In 3- Oy= log, e (2z+1)3…

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Q: dx = +C (x+1)² X+1

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Q: Let f (x) = 5sqrt (x+7)^9 (4x-1)/(6x+7)^4 Use logarithmic differentiation to find the…

A: Given: fx=5 sqrtx+794x-16x+74 To Find: To find the derivative of fx by using logarithmic…

Q: y = log4 x %3D .y = In(5x2 -4x + 8) %3D

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Q: Find the linearization of the function at a. 1. f(x) = x^4 + 3x^2, a = -1 2. f(x) = sin x, a =…

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Q: Q4. Use logarithmic differentiation to find y'. Vx²-1-sin x 3 x+2 (i) y = xsecx (ii) у %3D (iii) y =…

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Q: t2 sec-(t) y = cosh(sec t)

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Q: Find the second derivative of vx - Jy= 4 when x = 1. 2 1 -1 -2

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Q: Find the differential of the function. u = 3x4 + 4

A: The given function u=3x4+4

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

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

Q: Find the derivative of g(x) = J2x u²+1

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Q: 3 7 use log differentiation to differentiate to find y prime (dy).   y = sin(x)x

A: Given function y = Sin(x)x , here we need to determine y\'.Let us use logarithmic differentiation.…

Q: Find the derivative of the following: 8 f(x) = 3 (log5 ( – 2/x7 + x))* - e(v3³n²)

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

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