Two ships leave port at the same time. One sails south at 18 mi/h, and the other sails east at 24 mi/h. Find a function that models the distance D between the ships in terms of the time t (in elapsed since their departure. D(t) =

Q: Find the derivative of the function. t3 2 h(t) : to + 3 h'(t) =

A: Given function: Used formulas: Chain rule of differentiation, Quotient rule of differentiation,…

Q: Find the FIFTH DERIVATIVE Given: f (t)

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Q: s(t) = 5cos -t 4

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Q: If the position function of a moving object is S(t) =t - 3t + 2 meters from zero in t seconds, then…

A:

Q: Calculate the derivative.

A: h(t)=t(t+1)(t2+1)

Q: The size P of a small herbivore population at time t (in years) obeys the function  P(t)e^0.28t if…

A: The size P of a small herbivore population at time t (in years) obeys the function When P(t)=4000…

Q: The position of an object at time t is given by s(t) = -9 - 3t. Find the instantaneous velocity at t…

A: We can find the instantaneous velocity as below

Q: On her bicycle ride Fabiana's position (in km) as a function of time (in hours) is s(t) = 22t + 17.…

A: Fabiana’s position (in km) as a function of time (in hours) is given by

Q: At what time does f (t) attain its largest value?

A: Consider f(t) is any function. We know that function attains its largest or smallest value when the…

Q: Find the derivative df/dk. " f (k) = ek + a*

A: Find the derivative of the given function.

Q: Find the derivative of the function.

A:

Q: If an object is dropped from the top of a building, its position in feet above the ground is given…

A: Concept of differentials need to be used here.

Q: The median home price in a particular country over the period January 2010 to January 2015 can be…

A:

Q: Provide the equation of the line tangent to the given function at the specified point g(x)=ln(x^2);…

A: Given : gx = lnx2

Q: Find the directions in which t and decrease most rapidly at function in those directions.

A: given function fx,y,z=lnxy+lnyz+lnxz           =2lnx+lny+lnz             ∵lnxy=lnx+lny to find in…

Q: Find the derivative of the function.

A: Given function - g(s) = 6s3-23g(s) = 6s3-2-3Differentiating on both sides with respect to 's' -…

Q: The size P of a small herbivore population at time t (in years) obeys the function P(t)=600e^0.27t…

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Q: If a ball is thrown in the air with a velocity 48 ft/s, its height in feet t seconds later is given…

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Q: Find the second derivative of the function F(t) = 5tsin(r³).

A:

Q: Find the derivative of the function.

A: Given function is gt=lntt2. To find the derivative of the function. Solution: Quotient rule of…

Q: When is f (t) increasing at the greatest rate?

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Q: What is the decreasing and what is the constant

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Q: Find the derivative of the function.

A: We have to find the derivative of the function: st=14-5t-t2 We know the formula of derivatives,…

Q: The size P of a small herbivore population at time t​ (in years) obeys the function P(t)=600e0.25t…

A: Simply substitute P = 1200 and solve for t using Lograthim.

Q: Find an equation of the line tangent to the following curve at the point (a,f(a)). f(x) = 8 ex + 5x;…

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Q: Find the derivative of the function .

A: The given function is  ft=t23-t13+4

Q: What is the first derivative of the function h(t) = t/2t – 3

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Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 16 e*+…

A: Given function is fx=16ex+13x. At x=0, f0=16·e0+13·0=16 Therefore, point is 0,16 Differentiating the…

Q: A ball is dropped from a 200 foot cliff. If gravity is 32 ft/sec2, find the position function of the…

A: Given :- Initial height of ball (S0)= 200 feet Accelaration due to gravity(g) = 32 feet/sec2…

Q: In a certain city, the normal average temperature (in degrees Farenheit) is modeled by the function…

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Q: Find the derivative of the function. g(t) = 1/(4t+1)^3

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Q: Find the equation of the line tangent to the graph of f (x) = 1+ e-*for a. x = 0 b. x = -1

A: f(x) = 1 + e-x

Q: Find the second derivative of the function. t° + 9t +5

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Q: Find the derivative of the function w=e^(−5t)^5

A: We have to find derivative of w(t) with respect to t,where w(t) is given by

Q: The distance of a body travels as a function of time and is defined by x(t) = 18t + 9t^2. What is…

A: Given that: Distance travelled by the body is given by:             x(t)=18t+9t2

Q: The size P of a small herbivore population at time t​ (in years) obeys the function P(t)=1000e0.18t…

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Q: Find the first and second derivatives of the functions s = t2 + 5t - 1/t2

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Q: Find derivative of the 6tanx following function d d.x

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Q: Find the derivative of f (a) = e" (x² + 2).

A:

Q: Find the derivative of the function m: f(x)= e^x^3+4

A: Topic = Derivative

Q: Find the derivative of the function. 1 s(t) 2+ 6t - 5 s'(t) =

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Q: Use the sign pattern for the derivative dƒ/ dx = 6(x - 1)(x - 2)^2(x - 3)^3(x - 4)^4 to identify the…

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Q: T* dx from a=-1 to b-1 is an even function.

A:

Q: Find the derivative of the function. f(x)=4tan-1(e9x)

A: Consider the given equation

Q: Find the derivative of the function.

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Q: Find the derivative of the function. h(s) = −2√(5s2 + 3)

A: the given function is: hs=-25s2+3 we have to find the derivative of the given function.

Q: The size of P of a small herbivore population at time t (in years) obeys the function P(t) =…

A:

Q: a) Find the derivative of the function: T+ V3x f (x): 3x-1

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: The size P of a certain insect population at time t​ (in days) obeys the function P(t)=800e0.08e…

A:

Q: Find the derivative of the function g(t) = 23t / t2

A: Given: gt=23tt2 We know that ddxuv=vdudx-udvdxv2                                         ..1