The function P(t) = 24 + 8 sin(t) represents a population of a particular kind of animal that lives on a small island, where P is measured in hundreds and t is measured in decades since January 1, 2010. What is the instantaneous rate of change of P on January 1, 2030? Use the appropriate label for the derivative and include the units of this quantity. Write a sentence in everyday language that explains how the population is behaving at this point in time.

Q: Sketch the graphs of two functions that have the given derivative: f'(x)=2

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Q: ex = cosy

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Q: Find the thousandth derivative of  f(x)  = x e-x

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Q: +0.0001) – 1, tan(4 4. Which derivative is approximated by 0.0001

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Q: Find the second derivative of the function.

A: Given: fx=sec x To Find: The second derivative of the given function

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

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Q: Solve for the second derivative of the following implicit function

A: We can solve this as follows:

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A: Given function

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A: Here the function is y=8xr(x), where r(x)=5x We know that ln (ab)=ln a +ln bln (ab)=b ln a

Q: 26 Find the 155th derivative of (1 + x°)" at x = 0.

A: see 2nd step.

Q: Match the graph of the above function with the graph of its derivative. 0 ㅇ O 수 +

A: The given graph of the function is the graph of a semi circle. Or positive side of the circle.

Q: The function graphed above has: Positive derivative on the interval (s) Negative derivative on the…

A: Given that: Graph of a function.

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A: To determine the derivative of the function ex and domain of the derivative.

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

A: Consider the given function, fx=11+secx2 it can be also written as, fx=1+secx-2 now differentiate…

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Q: What is the Derivative of the function; y = log10(1 − 4 tan x)

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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.

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Q: 1, Find the first and the second derivative of f(x): f(x)=x

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Q: The size of a population of butterflies is given by the function. p(t)= 6000/(1+49(0.6)t) where t…

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Q: Find the second derivative of the function.

A: Given,         f(θ)=3tanθ

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Q: (# 11 Exam 1 Review) Find the equation of the line tangent to the graph of the function: f (x) =…

A: For the equation of tangent, we need to find the slope of the function at x=1.

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Q: Solve the second derivative ду? for f(x) = tan-1

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Q: Find the second derivative of the function. 9. g(x) = x-1 10. h(x) = sinx = (x)6

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Q: 2x-x² a. 2 logz e e*10* c. e*10* + loge

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Enumerate and explain the steps in finding the derivative of this function: y=1/[2*sqrt(x+3)]

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Q: Find the second derivative of the function. f(x) = sec x * "(x) = Noc

A: Please see the explanation below

Q: What is the derivative of: log x/(x+1)

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A: We have to find

Q: What is the instantaneous rate of change of the function f ( x ) = 5 /x  at x = 3 ?

A: Given,        The instantaneous rate of change of the function fx=5x at x=3.We know that,…

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A: Given: y = x-54 To find: Second derivative of the given function.

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A: Given: f(x)=log4(x2−x+3)

Q: 4. f(x)=

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

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Q: Solve for the derivative of the function using chain rule. 6. f(x)= cot(6x3+5)

A: Derivative

Q: Find the derivative of the function. h(x) = log4(x + 9) h'(x) =

A: Topic = Derivative

Exponential Growth Model

The relation that represents an exponential function is: