3. Find the implied domain for the following functions: (a) f(x) = Vx² – x – 6. %3D log, (x – 2) | (b) f(x) = x – 5 -

Q: Show that the following functions are harmonic in x and y: log√x² + y²

A: Solution

Q: Suppose A (*) =log(2-). What is the correct result of the derivative of h with respect to x? In (5)…

A:

Q: = (2),f %3D (त.ऋ) uj = (x)f 6(x+1) Break up the following function using laws of logarithms, then…

A: Given function is as below : f(x)=ln(6(x+1)x3)

Q: - for the following function: f(x)=log, dx 20. Find (2x+1)*

A:

Q: The logarithmic function f1x2  ln1x  12 has theasymptote x

A: Given f(x)=ln(x-1)

Q: B. Find the domain of each function. 1. f(x)=1+x 2. f(x) =1-V 3. h(x) = x-4 4. F(x) = x-1 5. G(x) =…

A:

Q: Sketch the graph of the function by plotting points. f(x) = log2(x) f(x) = log,(x) 22 y y 4 4 2 4 6…

A: We need to sketch the graph of the following function fx = log2x

Q: f (t) is of exponential order at infinity.

A: By fundamental theorem of calculus, we have f(t)=f(0)-∫0tf'(u) duAlso, since f' is piecewise…

Q: Find the function of the form y = log,(x) whose graph is given. y = y 1.0F 0.5 (4, 1/3) 1 2 3 4 5…

A: We have to find logarithm function

Q: Find the equation of the vertical asymptote f(x)=log(x+5)

A:

Q: II. Determine the derivative of the ff. logarithmic functions 7. y = 12x² log 8x 8. y = In 25x %3D…

A: Solution is below

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

A:

Q: Q3/ find the derivative D f(x) = x log5 @f(x) = (x+3) ² 2x+4 2 X

A:

Q: Find the derivative of the following function using logarithm laws. (2x2 + 3) y = (x – 1)2

A:

Q: Differentiate with respect to x:* y = log, (x) :() 2+ In x - In x Option 2 Option 3 2 - In x 1+ In x…

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

Q: D) Find the derivative of f(x) = log3 5x² + 1

A:

Q: Find the equation of the vertical asymptote f(x) = log(x + 5)

A:

Q: Find the first derivative of the following implicit function. x3 + y3 + 3 xy2 = 8

A:

Q: Differentiate the function with respect to x f(x) = 2* · log37*²-4

A: If hx and gx are two differentiable function and fx=hxgx Then f'x=gx×ddxhx+hx×ddxgx

Q: Find the derivative of the function f(x) = log23√(2x + 1)

A: To find derivative of fx=log22x+13

Q: 5. Find the derivative of the following Natural Logarithm functions f(x) = In(3x – 4) a. b. 2

A:

Q: Find the derivative of f( x ) = a° log (x + 7.5). f'(x) =

A: We have to solve

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

A:

Q: 4 f (x) = 3 (In (9x² + 7(log5(+Vx*

A:

Q: Suppose h(x) = log (2 -;) What is the correct result of the derivative of h with respect to x? A…

A: use logarithm to find the derivative.

Q: Differentiate the following and simplify: y= log, (sinhe") h(x)=3sinh(1–3x² )cosh(1– 3x² ) 1. 2.…

A: As per bartleby guidelines we only give first question answers.

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

A:

Q: Find the derivatives of the functions y = log2 (x2/2)

A: Given that y=log2(x22)

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

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: x-1 y = log XArctanx - Invx2 +1 = y x+1

A: We can find the second derivative as below

Q: Q3// By using logarithmic differentiation and with respect to independent variable x, find the…

A:

Q: Calculate the derivative of the following function. y=6 log 3 (x - 9) d 6 log 3 (x - 9) =D dx

A: d/dx [ f(x) ] = 1/ f(x) * d/dx[f(x)]

Q: 2. Compute for the value of x in a given logarithmic inequalities loga(x+1) > log:(x2). a. x > ½ b.…

A:

Q: FInd the Domain of these functions. f(x) = log7 (4x + 8) f(x) = ln(4x − 20)

A:

Q: 2 Show that the following functions are harmonic in x and y: 2 log√x² + y²

A:

Q: Find the equation of the tangent line to the graph of f(x) at x = 2, if 25 f(x) = 2.5 + log5 2 (x -…

A: For x=2 f(x)=2·5x+log5252xf(2)=2·52+log5252(2)f(2)=2(25)+log525f(2)=50+2f(2)=52 So the point is…

Q: Find Y for the following function: dx 3- y = log,(x3- x) 4- y = In 5- tan-1 V4x – 5

A: we have to find the derivative of the following

Q: Find the derivative of the function. y = log 6 V3x+7 3. O A. In 6 3 In 6 O B. 3x +7 In 6 (3x + 7) 3…

A: Given, y = log63x + 7Applying the log rule; logab = lnblnay = ln3x + 7ln6Differentiating with…

Q: What is the derivative of the given logaithmic function y = log3 (2x“)? 2 In (3z) 2 A. æ In (3) 2 В.…

A: Let's find.

Q: 36. Determine the x-intercept(s) of f(x)log2(3x-4)1

A: Rules:x intercept(s): is (are) the point(s) where the graph crosses the x-axis. In order to find the…

Q: 5. Prove if the following function is differentiable y = x loge-*

A: Given that: y=xloge-x

Q: 2) Write the derivatives of these four functions: a) 7 log8(x) b) 3ex c) 5(16x) d) 9ln(x)

A:

Q: 2. Find the derivatives of the following functions. a) y = (log2 x)3¬*

A: Given information: The function is y=log2x3-x. Calculation: Find the derivative of the function. Use…

Q: Find the function of the form y = loga(x) whose graph is given. y 1.0| 0.5 (2, 1/3) 0.5 1.0 1.5 2.0…

A: Function passes through the point (2,1/3) which satisfy the function

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

A:

Q: 3) For f(x) = log2 x and (x)=√x-4, what is the domain of f(g(x)) and g(f(x))?

A: The function f(x)=logx is defined for x>0 The function f(x)=x is defined for x≥0 Note: If logba=c…

Q: Find for the following function: 3- y = log,(x - x) 4- y = In2

A: It is an important part of statistics . It is widely used .