If ω'(t) is the rate of growth of a child in pounds per year,what does  ∫510 ω'(t)  dt   represent?

Q: (14) Use log differentiation to find the derivative of the function. Y = (sin (7x))*

A: Here, the given function is: y=(sin(7x))x Taking logarithm on both sides, we have: ln y=ln(sin(7x))x…

Q: Find the derivative of function.

A: To find the derivative of the given function                                                y=log…

Q: Obtain the Differential Equation from the family of lines whose slope is thrice the y- intercept.

A:

Q: Find the differential of the given function.

A: Given function - z = 1-2v+v4-23Differentiating on both sides with respect to v -dzdv =…

Q: In 2007, (when t = 0), world solar photovoltaic (PV) market installations were 2826 megawatts and…

A: Consider the given information. The initial value (t=0) is 2826. And the rate is 48%. St=S01+rt And,…

Q: L(x) = In(x)+log,(x)

A: Used formulas : ddx(logax) = 1x ln a ln x = loge xloge e = ln e = 1ln 5 =1.61

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos…

A: Given that y=cos6θ+15 Find dydθ Needed formulae: xn'=nxn-1 cos x'=-sin x ax'=a

Q: Find the first derivative:  y=log1o 5x+3/5x-4

A:

Q: find the second derivative of y=ln(e^x+e^-x)

A: Given query is to find the second derivative of the expression.

Q: Find the derivative, if y3 (log x)* + y = (log x)* +(sinx) -1

A:

Q: Find the general solution of the differential equation for interest compounded continuously,dA/dt =…

A: dA/dt=kA

Q: Find the derivative of the logarithmic function. 6 + y = In

A:

Q: Find a differential equation that corresponds to the given direction field.

A: This is a problem of slope field.

Q: The growth of a sunflower during the first 100 days after sprouting is modeled well by the logistic…

A: Growth rate at point of infection-

Q: What is the differential equation given functions?

A:

Q: find an equation of the tangent line at the point indicated. y = log2(1 + 4x−1), x = 4

A: We have to find an equation of the tangent line at the point indicated. the given function is…

Q: Find the derivative, if y = (log x)" +(sin x)™* -x %3D

A:

Q: Find the derivative of the function y = log4 (6x + 1)

A: Given information: y=log46x+1 Log rule: logab=lnblna

Q: what is the derivative to y= e^-1?

A: Given,

Q: Identify the differential equation that produces the slope field below. // ||// // 2.

A:

Q: Find an equation of the tangent line to the graph of the function at the given point.

A: Here given function as y=log102xory=log 2xlog 10 Differentiate with respect to x dydx=log2xlog…

Q: a- y= (cosx) (use logarithm differential)

A: To find dy/dx

Q: Evaluate the derivative. * d (log10 (x)) dx (In(10)) O Option 1

A: we have to find the derivative

Q: Calculate the derivative. 1 y = log 5x y' =0

A:

Q: A certain population is known to be growing at a rate given by the logistic equation = x(b – ax).…

A: Firstly find critical points. After that find second derivative , If second derivative less than…

Q: find the first and second derivatives of f(x) = ln (x+1)

A: f'(x)=1x+1 and  f''(x)=-1(x+1)2

Q: find the derivative of ln(3x^2+e^x)

A:

Q: An individual improperly disposes of 8 parakeets in a nearby woodland, where they begin to reproduce…

A:

Q: Derermine The FirST derivative of : 千irsT OF F) = x³ .16 V5メ-2 こSioN Expa usiNG Logalith mic Ex…

A:

Q: A population of wild horses is represented by the logistic differential equation dP/dt =…

A: Given: The logistic differential equation is, dpdt=0.08p-0.00004p2          (1) To find: A) The…

Q: Find the first derivative of = (ln x)* 4 y

A: From the given function; y=lnx4 We know that; The Power law: ddxxn=nxn-1 The chain rule:…

Q: The third derivative of the function is y = log 2x3

A: We can find the answer as below

Q: What is the first derivative of s(æ) = 4e"*.

A:

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

A:

Q: Describe the overall process of solving differential equations using the Laplace transform?

A: A differential equation can be solved in the following steps: Take the Laplace Transform of the…

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: What is the derivative of e' dt?

A: We use Leibnitz integral rule.

Q: 24. What does it mean to say that dV is an exact differential?

A: What do you mean by dV is an exact differential.

Q: 3. Find the derivative of (x² + 3) (3x – 3)² Y = Vrez+1 Hint: Use logarithmic differentiation!

A:

Q: The total number of reported cases of an illness in a large city days after the start of an outbreak…

A: According to the given information the total number of reported cases of an illness in a large city…

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

A:

Q: Find the first derivative of f = (h+2)² (2h+1) h²+3 V using logarithmic differentiation

A:

Q: What is the degree of the differential equation:

A:

Q: Find the first derivative of x² + 3xy + y3 = 10 implicitly.

A: The given function x2+3xy+y3=10

Q: Show that solving the logistic differential equation results in the logistic growth function

A: The given differential equation is dydt=825y54-y   with  y0=1. Solve the above differential equation…

Q: If an object's mass is changing at a rate proportional to its weight at a given time, does it make…

A: Two quantities are said to be proportional if they are increase or decrease in same manner. In such…

Q: Find the higher-order derivative. (4 log 2(x – 5)) dx2

A: Given, d2dx24 log2x-5

Q: What is the derivative of y = log, sec(e²x) Dxy = 2 e² tan (²) Dxy = 2 (log, e) e²x sec(e) tan(e) D,…

A:

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

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.