The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(z) = 1.8208e33872, where x =0 corresponds to the beginning of 1998. In what year did/will the exports reach $8.5 billion?

Q: Since the development of the iPod, the stock price of Apple has been growing rapidly and has been…

A: Given the development of the iPod that includes the stock price of Apple in which it grows rapidly…

Q: Which function has the same derivative function f(x) as g(x) = lnx + x² – x?

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Q: Find the function whose derivative is 1-e2x

A:

Q: Find the derivative of the f(x) = (x² + 1)³

A: To find the derivative of the function: fx=x2+13

Q: Find the second derivative of the function. Fx) = x In VR) + 9x f"(x) -

A: Answer and explanation is given below...

Q: What is the derivative of y = 3x²tan-1(x)?

A: ddxxn=n xn-1ddxtan-1x=11+x2 One have to use product rule here, which is ddx(uv)=vddxu+uddxv

Q: Suppose that you can calculate the derivative of a function using the formula f′(x)=3f(x)+1x. If the…

A: Derivative of a function using the formula f′(x)=3f(x)+1x and f(3)=6. We know that approximate…

Q: Calculate the derivative of the function. 8x +5 s(x)= 2x - 6

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Q: What is the average rate of change of the function f(x): = x² between x = -3 and x = 3?

A:

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = (8x4…

A: Given: y=8x4+53

Q: What is the derivative of F(x) = -4e2x ?

A:

Q: Which function has the same derivative function f (x) as g(x) = lnx + x² – x?

A: we have to find derivative

Q: Find the second derivative of f(x) = (5+7x)e5". f" (x)

A: Topic :- Differentiation

Q: Find the derivative of the function. f(x) = x2(x − 2)7

A:

Q: Solve for the second derivative of f(x)=2x-2/x+5

A:

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = (x2 +…

A: The given function is ;  y=x2+9x-2  ...........................(1) differentiate with respect to x

Q: What is the first derivative of p(x)=3^(x^5)?

A:

Q: Find the derivative of f(x) = log35x2+1

A:

Q: what is the second derivative of  f(x) = 3(3x^3+2x^2)^10

A: We first find the first derivative using the power rule and chain rule.…

Q: Find the derivative of f(x) = log3 5x2 +1

A: Find the derivative of fx=log35x2+1

Q: Find the second derivative of the function. f(x) = e-x3/3

A: Given:fx=e-x33Differentiation formula:ddxex=ex.1

Q: Find the derivative of the function f(x)=x-2/2+x square root

A:

Q: What is the inflection point of the function f(x) = x5 ln(x)?

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Q: What is the second derivative of ƒ(g) = 12g² + 15g² +26g³?

A:

Q: Find a function whose square plus the square of its derivative is 1.

A: To Find a function whose square plus the square of its derivative is 1.

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = (x2 +…

A:

Q: Find the third derivative of the function y=e2xlnx.

A:

Q: Use the definition of the derivative, to find the derivative of y (x) x +1 x + 4 (x + 4) 1 (x + 4) 3…

A:

Q: What is the derivative of f(x)= -3

A: Given f(x) = - 3

Q: Find the second derivative of the function. In(x) f(x) 6x2 f"(x) =

A:

Q: The number of U.S. citizens aged 65 years and older from 1900 through 2050 is estimated to be…

A:

Q: f(x) e3x+1 lnx³

A: Here we have two functions in the right hand side. That is f(x) is the product of two functions. So…

Q: Find the average rate of change of f(x) = 3x2 - x from x1 = -1 to x2 = 2.

A: The given function is fx=3x2-x.

Q: What is the first derivative of f(x) = √√x² + 2x − 1?

A: Given the function,    fx=x2+2x-1

Q: What is the difference of antidifferentiation and anti-derivative?

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Q: A pharmacologist studying a drug that has been developed to lower blood pressure determines…

A:

Q: Find the second derivative of f(x)=x4.

A:

Q: Because of the popularity and power of smartphones, demand for wireless communication is growing…

A: Given:

Q: The total expenditures (in millions) of current dollars for pollution abatement and control during…

A: Here we find the total expenditure.

Q: Evaluate the second derivative of the function below at (1, -2). y² = x³ = x + 1 -

A: To evaluate the second derivative of the function at the given point.

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,…

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

A: Given function,  f(x) = xe-x  To find the thousandth derivative of f(x)

Q: On the basis of data for the years 1911 through 1991, the expected life span of people in a country…

A: First find the number of years x from 1908 to date of birth of the person 1966 than put that x in…

Q: 33. Solve for the second-order derivative of the function below. Y = x 3x3 За

A: Differentiate two times wrt x

Q: find the average rate of change of f(x) = -x3+3x2 from x=-1 to x=4

A:

Q: Find the second derivative of f(x) = 3e³* – 8e** -6.x 10)

A:

Q: What is the average rate of change of f between x=3 and x=10

A:

Q: A company has a stock valued at A, in millions of dollars, that changes at a rate given by dA dx =…

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.