Find an approximate value for x (to 2 decimal places) if 5=(3lnx) - (lnx/2) . Find y'' if y = ln(1+1lnx).

Q: y = In (x* + 5)³

A:

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: find the derivative:  y = ln (8x^3 – 2x) – 2x

A: According to the chain rule of differentiation if fx and gx is the differentiable function then,…

Q: 3.

A: Indefinite Integration

Q: 1. у %3D х+/x

A: Topic = Derivative As per guidelines , At  a time only one question can be answered out of different…

Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: An experimental forest is to be grown by planting 3000 trees each year on the same day of the year.…

A: Let i = number of years = 0, 1, ... , 10 and the number of trees planting in the starting of each…

Q: A quantity with an initial value of 220 grows continuously at a rate of 9.5% per hour. What is the…

A: Consider the provided question, Given, initial value = 220  Rate, r = 9.5% = 0.095 per hour t = 225…

Q: 5th derivative of y = log x^5 to the base 2

A:

Q: 2.) Find 1st derivative of y = e-'In (x-1)

A:

Q: For y=ln2x, determine the equation of a tangent line parallel to 2x-3y+1=0

A: here we find the equation of a tangent which is parallel to 2x-3y+1=0. y=mx+c slope = m.

Q: Find the equilibria of the differential eq

A:

Q: find derivative y=square root of (1+ x times e^-2x)

A:

Q: Find the antiderivative of antiderivative of x2(ln(10x))2

A:

Q: Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

A: the fiven function is f(x)=ln(x)

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

A:

Q: Find the first derivative of: y = sinh e2" O y e2 cosh e2# 2e2" cosh e2" O y' 2 cosh e2 O y = cosh…

A:

Q: 3. Find the second derivative of y= xlnx

A:

Q: Log Activity CALL l.y=log4 (3x2 -5x) In 9x4 2.y= 3.y= Inx3 X-5

A:

Q: A certain radioactive material is known to decay at a rate proportional to the present amount. If…

A:

Q: 11) Find the first derivative of y = (lnx) 4

A:

Q: Find the derivative of n^(ln⁡(cosu)). Where n=822

A: Given information : nlncosu Here, n=822. we have to find the derivative of given function.

Q: A quantity with an initial value of 200 grows continuously at a rate of 4% per second. What is the…

A: To find: The value of quantity after 1.55  minutes. Given: The initial value of quantity is 200 and…

Q: A radioactive element is known to decay at a rate proportional to its present mass. Initially, there…

A: Given: A radioactive element is known to decay at a rate proportional to its present mass.…

Q: What's the derivative of ln(ln(ln(lnx^3)))

A:

Q: A quantity with an initial value of 310 grows continuously at a rate of 8.5% per second. What is the…

A:

Q: Find and sketch an exponential equation of the form y = Ce^kx that passes through the points (0,8)…

A:

Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

Q: Determine the derivative: y = log (3x2) (01)प य log (3) ** In(10) 6 log (Sx) r In(10) Oy= 18x In(10)…

A:

Q: 1. For a certain radioactive element decays at a rate of 37.7% per day (tis measured in days). How…

A: We need to find time.

Q: A colony of bacteria with originally 100 cells has now grown to 900 in 2 hours. Assuming the rate of…

A:

Q: Find the equation of the line tangent to the graph of y = 6 ln(x) at x = 3. Tangent Line: y =

A: We have to find the slope of tangent at first.

Q: A radioactive element is known to decay at a rate proportional to its present mass. Initially, there…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: A quantity with an initial value of 310 grows continuously at a rate of 8.5% per second. What is the…

A:

Q: quantity with an initial value of 220 grows continuously at a rate of 9.5% per hour. What is the…

A:

Q: find the derivative of y with respect to the givenindependent variable. y = log2 (8tln 2)

A: We first expand the equation using the addition property of log and the change of base property.

Q: proportional

A: We will solve the problem.

Q: Find the second derivative of 2x^2 ln (1/x^2)

A:

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

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A:

Q: Find the differential of the function y=lntan2x at x=π/8.

A: Given: ,at x=π/8 Differentials are infinitely small quantities. Use the term for differentials as…

Q: 4. y=ln(4x' +5)

A:

Q: Find the nth order derivative of the cube root y=3√x.

A: We first find the first three derivatives using the power rule

Q: Find and sketch an exponential equation of the form y = Cekx that passes through the points (0, 8)…

A: Given an exponential equation of the form y=Cekx that passes through the points (0,8) and (3,4). To…

Q: A radioactive material decays continuously at a rate proportional to the amount present. After 2…

A:

Q: It is projected that x years from now the population of a certain city will be changing at the rate…

A:

Q: 8. Determine the half-life of the substance if an initial 150mg has decayed to 50mg in a an of 20…

A: Given query is to find half life and the time when 95% amount decayed.

Q: The half-life of plutonium 239 is 24,200 years. Assume that the decay rate is proportional to the…

A:

Q: Find the equation of the tangent line to the curve y = log(x2-3x+1) at the point (3,0)

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: