SYNTHESIS 23. Differentiate: y = x(ln x)² – 2x In x + 2x. %3D d²y log 3 (3x² + 4). Find dx 24. Let y = 2.

Q: dy (x² + 1)? if y = 2) Find dx (x² – 1)³ a) without the aid of logarithmic properties b) using…

A: Here we have to find the the derivative of y

Q: 8. In V5x 3 y z2 9. log. V xt 10. loga Va b5

A:

Q: 1. logx = 2 %3D 2.ln(x + 1) = 5

A:

Q: Log(X^3Y^2Z^7)

A:

Q: (iv) log, r – log,(r – 1) = ; (v) 41-z = 32r+5 () -- (vi) 2x In = 0

A:

Q: s) Use the properties of logarithms to find dx y = In 4] sin' (3x) 5* √√x² +1

A: We can solve the derivative of 'y' as below.

Q: 3. Use Log Rule to integrate. a. Sor5 Sdx а. бх-5 b. S; -dx x(lnx)²

A:

Q: question 24

A: The given function is,

Q: (x² + 1)? dy if y Find dx (x² – 1)³ a) without the aid of logarithmic properties b) using…

A:

Q: x° -1 The value of the integral dx, (a > 0) is log x

A:

Q: 2. Differentiate: a) y = log2(3x) %3D 2 b) f(x) = –7 log(x²) %3D

A:

Q: Differentiate the function

A: Before we get into solving the question, let's look at the two derivtives shown on the white…

Q: dy/dx of log5(y2-y) + csc-1 (x/π) = -3y

A:

Q: To evaluate the integral +logx) dx we use the substitution O a. -t O b. (1+logx )²=t O c. (1+Jogx)=t…

A: Please see step 2 for answer

Q: dy Use the properties of logarithms to help perform dx COs x y = ln 3 – 5x2 - dy dx ||

A: As we know that ddxlnx=1x

Q: For a certain drug. the amount y(t) remaining in the blood after t hours satisfies y'=-0.12y with…

A:

Q: Find , given y = log(ev+x²). dy dx

A: Given y=logex+x2  We find dydx The differentiation formula of logarithm is ddxlnx=1x and the power…

Q: Find y by logarithmic differentiation. y=x²X A O y = 2 In x+2 2 In x-2B O y = x²* (2 In x+2) .C O y…

A: Use log to differentiate

Q: 6log3(t + 4) = 36 %3D log3(t + 4) = %3D t = II

A:

Q: How is the graph of y =log(x) transform to produce the graph of y=log(2x)+3

A: Given graph of y = log(x), transform it to get the graph for y = log(2x) + 3.Let us first discuss…

Q: Solve this logistic function. Find the inflection point (t, N). dN/dt = kN(1-N/M)

A:

Q: ( 3x+log; x dx = ? ||

A:

Q: hical Method Example (2) s (x ) = -- 1 log x x e[1,4] %3D y,(*)= 1 & y (x) = logx 1.5 y,(x) 0.5 ,(x)…

A: Given equation is  F(x) = 1/x - log x

Q: Use the logistic growth model f(x) = 150 %3D 1 + 7e-2x Find the carrying capacity.

A: Use limit to determine the carrying capacity for f(x).…

Q: e2x+sin x-1 b. lim x-0 log(1+6x)

A: L'Hospital rule states that when the limit is of 0/0 form then differentiate the numerator and…

Q: dx 2* +1

A:

Q: Find dy/dx if y=log(-4x^2+2)

A: To find the dy/dx of the given function.

Q: Q3\ Solve for x: a. log(20x + 1) – log(x – 2) = 2 b. In(x - 2) + 2 in Vx+ 3 In6 %3D

A:

Q: Find d/dx(2x) Type ln(x) for the natural logarithmic function.

A: Given query is to find the derivative of 2x.

Q: Combine into a single logarithm. In(x – y) – 2 In(x² + y²) OIn (x-y)3 In (x²+y²)* In Va-y) (x²–y²)?…

A:

Q: Evaluate log2(x²) dx In(2) -log2(x²) + C 4 In(2) log2(x²) + C n(2) (log.(r2))2 (log. (x2))2 1r 4…

A:

Q: II. Determine the derivative of the ff. logarithmic functions 1. y = 25 In 5x 2. y = -10 In 3x4 3. у…

A:

Q: 1 dy Find dx if y = (x²+1)(x+3)2 x >1 x-1 Hint: (The properties of the natural logarithm can be…

A:

Q: Pr. #2) Solve for y' = by logarithmic differentiation. e sinh(3x + 1) y = (2x + 1)4 5x –1

A:

Q: Differentiate the function T(z) = 2z log2 z.

A: The given function is,

Q: 2 In 2 log2 x dx 7- S

A: Here I am attaching image so that you understand each and every step.

Q: 4.) Find y': Given:y = x²(3 cosh x - 1) 5.) Find y': Given: y = log, csc h (6x³)

A:

Q: Find d (7ª). Type In(x) for the natural logartihtm function. dx

A: Given query is to find derivative if the expression.

Q: dy by first using algebraic properties of the natural logarithm dx Find (x + 6)(x + 8)* (x +3)*(x +…

A:

Q: dy Example 1: Solve x- +y= logx dx

A:

Q: loge (cos x) e. lim x V1+x2 -1

A: e.limx→0logecosx1+x2-1

Q: 3. log (x²+x)-log.(x-1)-2 А. 2 Oi J. оо о で В. 16 C..X D. - 16 -

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: log 3= x loghs y log1s j tye. Show in x ad ニ

A: Given,          log9=x  and  log4=y

Q: 12. Evaluate a) xcos2x dx, leaving your answer in terms of n. b) dxusing the substitution u 3x + 4…

A: Integration.

Q: 1+logx 2. =D1. %3D 1. 196 16. Solve for x, 5-log:

A: We have to solve for x .

Q: Find dy dx given (х* + 3x — 1)° /1 – 3x³ y , by using property of logarithms.

A:

Q: Differentiate : a. y=log2√x b. y= 2x^(3x) c. y = (x+1)^x

A:

Q: 12 %3D 5. (i) By using the substitution u = 1+ cosh x, rcosh-12 tanh x dx, 1+ cosh x evaluate…

A:

Q: 4. y = log v2x + 55. y = In(2x + 1)*6. f(x) = In(x +3)* %3D

A: topic - derivative of a function