If f (x) = /In(x²) + x², what is the value of f'(1)? %3D

Q: Five mice in a stable population of 500 are intentionally infected at r= 0 with a contagious disease…

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Q: It is estimated that t months from now, the population of a certain town will be changing at the…

A:

Q: Find the derivative of f( x ) = 2° log3(z + 2.5) f'(x) =

A: The first derivative of the function is . The product rule of the differentiation is .

Q: 2. Show a graphical method of approximating the instantaneous rate of change at x = 3 for the…

A: You must have idea about what is the basic difference between instantaneous and average rate of…

Q: Use central difference method to estimate the 1st derivative of the following function at x = 2 and…

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Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Given that , The radioactive material is known to decay at a rate proportional to the amount…

Q: What is the first derivative of s(x)=(6x)^3x at x=3? Enter an exact answer in terms of a natural…

A: We will take the logarithm with base e and then find the derivative with respect to x and then…

Q: If the sign of the first derivative function is positive, the main function f(x) is decreasing.

A: We have to tell If the sign of the first derivative function is positive , the main function f(x) is…

Q: 10. S(2x – 3) dx e 2x2 - ебх

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Q: find derivative y=square root of (1+ x times e^-2x)

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Q: Find the anti-derivative of: S(3x* – 6x)° (2x³ – 1)dx

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Q: Find the derivative of ln(2x2)+ln(2x)+1/3 where x=1

A: Given,           The derivative of  ln2x2+ln2x+13 where x=1

Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

Q: s projected that x years from now the population of a certain city will be changing at the rate of…

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Q: 1. f(x) =In (ta n"x)

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

Q: 8. Create the equation of any function where the instantaneous rate of change when x = 1 does not…

A: Create the equation of any function where the instantaneous rate of change when x = 1 does not…

Q: If the total revenue function for a blender is R(x) = 41x – 0.01x² where x is the number of units…

A: Given that, the revenue R (in dollars) for a blender is given by  R(x) = 41x - 0.01x2 where x is the…

Q: A storage battery discharge at a rate which is proportional to the charge. If the charge is reduced…

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

A: we have to find the derivative

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: What are three methods that can be used to estimate the instantaneous rate of change in g(x) at x =…

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Q: Find the derivative of the function. Y= q56* In(2)ln(5)ln(6)· 3*. 5".; 2:56*+1+x

A: Given problem:-

Q: A storage battery discharge at a rate which is proportional to the charge. If the charger is reduced…

A: Solve by making equation

Q: What is the derivative of: y ln x − x ln y = 1

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Q: 3// By using logarithmic differentiation and with respect to independent variable x, find the…

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Q: What is the first derivative of the expression (xy)× = e?

A: See the details solution in below

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 of the function  f(x)= e^-3x ln x

A: Given function is

Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

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

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Q: Find the equation of the tangent line to the graph of f(x) = 4^(x/ln2) at the point where x is ln16.

A: We find dy/dx to find the slope at x.

Q: Find the derivative of the function y, below. 9x(ln x + In 2) – 8x + v2 %3D

A: first, simplify the function  y=9xlnx+ln2-8x+2 y=9xlnx·2-8x+2 y=9xln2x-8x+2

Q: What is the derivative of the function  x^8(ln(x)), and what can I substitute for x to make the…

A: We have to find derivative dy/dx and point where dy/dx =0y is given below:

Q: solve the first and second derivative of Y= (1+lnx)  /  x

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: Find the equation of the line tangent to the graph of y=(x^2−x)ln(7x) at x=2. Round to three…

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Q: proportional

A: We will solve the problem.

Q: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

A: Given function: fx=-2x2-x

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Q: 4x dx

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Q: 1 erivative of x²+2

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Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

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Q: 10. Solve for the derivative of y IMPLICITLY 22 + vx³ + 2y= y²

A: Topic =Derivative

Q: What is the derivative of the function  x^8(ln(x))?

A: To find the derivative of the function x8(ln(x)) as follows.Redefine the function as follows.

Q: Find the first derivative of:   f(x) = ln [(5x+2)1/2 / csc(x)]

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Q: It is projected that x years from now the population of a certain city will be changing at the rate…

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Q: Find the derivative of f(x)= ln x^2/x^2+1

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Q: A culture of bacteria grows at a rate that is proportional to the present number. It is found that…

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Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

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