Disprove the statement ln(xy) = (ln x)(ln y) by, a) Letting y equal a positive constant of your choice, and b) Using a graphing utility to graph the function on each side of the equal sign. The two functions should have different graphs, showing that the equation is not true in general.

Q: Let y = 2 ln x - 1/2x then the first derivative is....., the first order condition is..... and the…

A: Given: y=2 ln x-12x To Find:  To determine the first order derivative.To determine the first order…

Q: When solving ordinary differential equations, the derivatives are approximated with O grid and…

A: In general, a finite difference approximate to the value of some derivative of a function at a point…

Q: find the derivative of the log functions: y = ln(x√x2 – 6) f(x) = ln(2x/x+1)

A:

Q: 1) Using method of logarithmic differentiation, find the derivative of y = (2.x² + 1)(2=-3)

A: Given: Y = (2x2+1)(2x-3)

Q: Find the derivative of the function. f(x) = ln(5+e^x/5-e^x)

A: Use derivative formula :- f(x) = lnx then derivative f'(x) =1/x

Q: In 5 7x 78. y = log5V3x + 2

A: We have to solve

Q: Find the first derivative of the following functions Y = x5 e-3 ln x and Y = ln √ [ (x – 1 ) / ( x…

A: Solution is given below:

Q: Solve using implicit differentiation.  e^3x/ e^2y = sin y

A:

Q: Find the derivative of the logarithmic functions: y = ln(12x-4)

A: Solution of given question is written in below steps.

Q: You are setting up a "continuous annuity" trust fund. MOney is continuously transferred from your…

A: answer is in next step

Q: e first derivative for the +1)(x +2) 2)

A: Find the first derivative. y=(x+1)(x+2)(x-1)(x-2)

Q: Without using a graphing calculator, how can I show the function 1-ln(y )= z in a graph and its…

A: Without using a graphing calculator,  Show the function zx,y=1-lny in the graph and its traces.

Q: Find the indicated derivative and simplify. [3x log x³] dx [3x log x³] = dx (Type an exact answer.)

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the indicated derivative and simplify. [6x log x°] dx [6x log x ]= 125 dx (Type an exact…

A:

Q: Suppose that you now have $10,000 and that you expect to save an additional $4000 during each year,…

A: Given that, you now have $10,000 and that you expect to save an additional $4000 during each year,…

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

A: The given function is, y = x.Take log on both sides of the function.

Q: Can you help me with this problem step by step?

A: The equation is given by

Q: 1. a) Use Logarithmic differentiation to take derivative of (x3 + 1)4 sin? x y = f(x) =

A:

Q: A savings account earns a 4% annual rate, compounded continuously, and $500 per year is withdrawn…

A: Here yt denote the value of the amount after t- years.

Q: Activity 2 Find the first derivative of the following: 1. y = ln (12x) 2. y = sin-¹ (x² + 3) 3. y…

A:

Q: Find the derivative: y = x [ln(x) - 1] O ln(x) - 1 о O x ln(x) O In(x) O 1 + In(x)

A: Given y=x[lnx-1]To find dydx:

Q: Find the derivative of the function. h(x) = log2(x2 + x)

A: Given function is : hx=log2x2+x To find the differentiation of a given function.

Q: )=1/x. Using this, compute the

A:

Q: (a) Use logarithmic differentiation to find the derivative of the function. y (In x)seca (b) Find an…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: xsinx sec (x)

A:

Q: 5. (i). Find the dx for the function y = (tanx)secx* using logarithmic differentiation.

A:

Q: e3x _e-3x Y = e3x +e-3x]

A:

Q: Find the slope of the tangent line to the exponential function at the point  (0, 1). y = ex/3

A: Slope of tangent line is derivative of the given function at that point.

Q: 11.The half-life of a radioactive material is the time required for an amount of this material to…

A: Solve the differential equation Q'=-rQ to obtain a general solution Q(t). Q'=-rQdQdt=-rQdQdtQ=rQ…

Q: 3// By using logarithmic differentiation and with respect to independent variable x, find the…

A:

Q: Find the derivative of the function. f(x) = ln(x2 + 1)2

A:

Q: Find the derivative of the function. h(x) = ln[(−6x + 3)(x + 3)]

A:

Q: The derivative of the function y = cos(x In 3) log3(sin x) is:

A: Given,            y=cosxln3log3sinxTo find : The derivative of the given function.

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given: y=sinh(3x2 ln(1+3x)) Use chain rule for derivative: ddx(f(g(x))=f'(x)ddxg(x) And uv rule for…

Q: Find a number such that the tangent line to the graph y= log,(x) at x = a is parallel to the tangent…

A: The objective is to find the value of a

Q: If x and y are measurements of certain parts of an organism, then the rate of change of y with…

A: Formula used: The differential equation can be equivalently expressed in the form g(y) dy=f(x)dx…

Q: Find the first derivative of y = (ln x)* .3 Find the first derivative of f(x) = 3x e

A:

Q: Find the derivative of the function. f(x) = ln(8x + 9)

A: Given, f(x) = ln(8x + 9)  We have to find the derivative of the function.

Q: 1. Use logarithmic differentiation to find the derivative of the function. y = x4 cos(x) 2. Use…

A: Here we have to find the derivative of the given functions using logarithmic differenciation.

Q: Find an equation of the tangent line to the curve at the given point. y = ln(x2 − 3x + 1),      (3,…

A: To Find an equation of the tangent line to the curve at the given point. y = ln(x2 − 3x + 1),…

Q: Find the first derivative y= ln(3x)

A:

Q: Using logarithmic differentiation, Show that y (x)= xa2" e®has no stationary points other than x =…

A:

Q: Question The derivative of the function y = cos(xln 3) log3(sin x) is:

A: We will find the derivative.

Q: Find the derivative of the logarithmic functions: y = ln ( 4x^3 - x^2 + 1^2)

A: Application of derivatives

Q: Determine whether the equation is true or false: ln x + ln(2x) = ln(3x). Where possible, show work…

A: Our Aim is to determine whether the equation given below:-ln (x) +ln (2x)=ln (3x) -(i) is true or…

Q: Find the derivative of y = log7 (2 -3x) .

A:

Q: Use the log rule of differentiation and differentiate y with respect to x.  y = ln( 8 + ex 8 − ex

A: given function

Q: find the equation of the tangent line to the graph of the function y = ln(x^2) at the point (3, 1).

A:

Q: Find an equation of the tangent line to the graph of (log æ)cosh(a-10) , x >1 at the point where x =…

A: Given equation is  y=log xcosh (x-10), x>1 at x=10

Q: A body at a temperature of 50° F is placed outdoors where the temperature is 100° F. If after 5…

A:

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.