· The carbon monoxide level in a city is given by c(p)=0.04p" +2 ppm (parts per million), where p is the population of the city (in thousands). After t years, the population of the city is predicted to be p(1)=12-31 +r thousand people. a) Find c'(p) (the derivative of c with respect to p). How fast will the carbon monoxide level increasing with respect to population when the population is 25 thousand people? b) Find p'(t) (the derivative of p with respect to f). How fast will the population of the city be increasing after 4 years? c) Write out the composition function c(p(t)), then use the chain rule to find c'(t) (the derivative of c with respect to t).

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: y = In (x* + 5)³

A:

Q: Determine the first derivative of the ff. function y = tan(ln(cot(x² + 3 ln 3x)))

A: Chain rule of differentiation: f(g(x))'=f'(g(x))g'(x) Formulae used: ddxtanx=sec2xddxlnx =1xddxcot…

Q: Find the derivative of the logarithmic functions: y = ln (tan^2 θ )

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: A second derivative Findd2y/dx2 if x2 + y2 = 1.

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

A: Substitute the values of (x,y) in the function given and find out the equation.

Q: find the derivative of the function  y'=ln(squared root of x^2-4) and  y=ln IsinxI

A: The given function is y=lnx2-4. Obtain the derivative as follows.…

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

A: Given:

Q: a.) A sphere shaped balloon is being inflated with a rate of 800 cm³ per minute. When the radius of…

A:

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

A: The equation is given by

Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cose

A: The given function is : s(θ)=200sinθcosθ We need to find the derivative in two ways.

Q: 14) Find the first derivative of f(x)= 2*2*

A: The derivative of ax is axlna. The derivative of xn is nxn-1, where n is any integer. The chain rule…

Q: Find an expression for the derivative of the exponential function y=ex using the definition of…

A: To determine the derivative of exponential function y=ex using definition of derivative.

Q: ind the derivative of y=(x-1)(2x-x2)1/2 - arccos(x-1)

A: Given function: y=x-12x-x2-arccosx-1

Q: 9. If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters)…

A: Given- If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in…

Q: 4. Find an equation of the tangent line to the graph of f(x) = ln(x ^2 + 4) at the point (2, ln(8))

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

A:

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

A:

Q: This is determined by the largest derivative, or the highest level of differentiation, present in a…

A: The highest level of differentiation present in a differential equation is known as "order" of the…

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: Find the first derivative of y = 1 using the Chain Rule. (1– x4)6

A: These questions are related to differentiation, We will solve them using given information.

Q: Find the derivative of y with respect to x Y=5 ln (3 ln x)

A: Given, y=5 ln (3 ln x) We have to find derivative of y with respect to x.

Q: Find the derivative of y with respect to x. y = csc-1(x5 + 1) ; x > 0

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 second derivative of the function. g(x) = √x + ex ln x

A: Consider the given function gx=x+ex lnx Now, differentiate the given function with respect to x…

Q: Find the derivative y=ln(2x^3+6x-1)^3

A: y=ln2x3+6x-13 take derivative y'=ddxln2x3+6x-13 y'=12x3+6x-13ddx2x3+6x-13

Q: ii) y = e**-2x + x²-e

A: We need to find the first derivative of the following y=ex3−2x+x2−e so we we need to find value of…

Q: Find the second derivative of y=cos32x Find the derivative of x+5/x2-1 Differentiate y=ex-cosx2 The…

A: 1) Given: y=cos32x On differentiating y with respect to x, dydx=ddxcos32x       =3cos22x×ddxcos2x…

Q: 1. Use logarithmic differentiation to find first derivative of y = xsinx

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: Solve the problem and give a detailed solution. Find the 3rd derivative of y = ln(cos(e3x))

A: Note ÷ I have used chain rule and product rule multiple times. Please look carefully.

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: 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: Compute the derivative ln(ex+1) / 2x+1

A:

Q: Find the equation of the tangent line to the curve given by f(x) = x2 ln x at the point  (1, 0)

A:

Q: gives a good approximation, where t is time in years since 2007. Find the derivative function R'(t).…

A: The model representing the given data is defined by the function Rt=0.25t2-t+29 gallons, where…

Q: The tangent line to the graph of y=f(x) at the point (7,55) has the equation y=8x−1 (a) Find f′(7)…

A:

Q: Find y'' by implicit differentiation. 5x2 + y2 = 4

A: Implicit differentiation

Q: 1. Find the second derivative of y = sec-'x+ csc-!x. a. 0 b. C. +x+ d. -1 2. е.

A:

Q: Find the instantaneous rate of change of f(x) = x* at x = 3. %3D Find the derivative of g(x) = x + x…

A: 1) Given, f(x)=x2 at x=3 Use the definition of instantaneous rate of change: The instantaneous rate…

Q: 2. 1950, a seed was planted same as the year as Jilian was born. When she celebrated her debut, the…

A:

Q: Find the derivative of the function h(x)= ln(5x+1/7x-2)

A:

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

A: We have to find the first derivative of given function.

Q: Example 2.35: Using Implicit Differentiation to Find a Second Derivative d'y dx Find if x +y² = 25.

A: Explanation of the answer is as follows

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: 5. Find the 25" derivative of y= In x.

A: We have to find the 25th derivative of y=ln(x)