1. (x) is increasing. 2. f'(x) < 0 3. The graph of fis concave downward. C2 Cs C6 C7

Q: Q2 find the derivative of the following: 1) y = 2stn²(5x) ,2) y = Inx'n cosh 5x ,3) xsin¬14y = y…

A:

Q: 8. Suppose the derivative of the function y = f(x) is y' = (x – 1)*(x – 2)(x – 4). At what points,…

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Q: 1 What is the lineur is The slope of the line tangent to the graph y = cos x at the point x =…

A:

Q: 2. At x 3, the tangent line to the graph of a function f (x) is y = 4x + 5. What is f'(3)? How do…

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Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

Q: Suppose that antibiotics are injected into a patient to treat a sinus infection. The antibiotics…

A: The concentration is given as , Ct=e-αt-e-βtβ-α where α and β are constants with β &gt; α &gt; 0.

Q: 9. Suppose for sume funchion f we have its derivative, f'x) = e*sin(x), on the %3D interval o< x<…

A: We can use application of derivative in order to solve the given problem.

Q: Use the first derivative test to find the location of all local extrema in the interval for the…

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Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…

Q: 4. The process of finding a general formula for the slope of a line tangent to a certain curve is…

A:

Q: Suppose that the differentiable function y = ƒ(x) has an inverse and that the graph of ƒ passes…

A: Given,

Q: Please use Limits this is under calculus section

A: When x = 2, y = g(x) = 4 / (x - 1) = 4 / (2 - 1) = 4Hence, the point of tangency is (2, 4)

Q: The fifth-order partial derivative ∂5ƒ/∂x2∂y3 is zero for each of thefollowing functions. To show…

A: The given function is f(x, y)=y2-ysinx-x4.

Q: Find the derivative of the function by the limit process. h(s) = −2 (square root of x)

A:

Q: 2. Find the derivative of y= ecos{/x+3) Solution:

A: Topic:- derivatives Note:- as per our guideline if more than one question uploaded than only first…

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

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

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))

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Q: Use the definition of a derivative to find f'(x) and f"(x), when f(x) = 2/x. I got f'(x) = -2/x2,…

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Q: A company wants to accumulate Tk. 100000 to purchase replacement machinery 8 years from now to…

A: Solution is given below:

Q: True or False The graph of y = cos x is decreasing on the interval (0, π).

A: True or False The graph of y = cos x is decreasing on the interval (0, π).

Q: If f(x) is odd function, then the derivative of y=sinh (f (-x)) equals Select one: o y'=Xf'x) – f x)…

A: Differentiate wrt x

Q: 1. Use forward, backward and central difference to estimate the first and second derivative of f (x)…

A: Given function is fx=coshx and x=2 Step size h=0.01 We have to estimate the first and second…

Q: 3. The derivative of f(x) = In x at x = 3 when h = 0.002

A: 3) To find the true error and relative error of the function: f(x)=ln x, x=3 &amp; h=0.002

Q: a.) z= 5.

A: We will find the second derivative of the given function in the following step.

Q: i. Show with the aid of Argand Diagram, where Ln(z³ + 3) is analytic . ii. Determine the derivative…

A: The given complex function is fz=lnz3+3.

Q: 2. Given that y= -- Use a limit to find the instantaneous rate of change of y with respect to x at…

A:

Q: If y- sin x and yn) means "nth derivative of y with respect to x", what is the smallest posilive…

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Q: 1. Solve the first derivative of f(x) = e-2x In x at x = 0.5 using forward finite-divided difference…

A: To find the first derivative of the function f(x) = e-2xlnx at x = 0.5 using forward finite-divided…

Q: the sales of a book publication are expected to grow according to function  s=300000(1_e-0.06t),…

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Q: 8. For the function: 2 f(x) x +3' use the limit definition of the derivative to find f'(x).

A:

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: In our last class discussion we found that a function y(x)= x* indicated by taking y"(x) = 0 that…

A: Definition: The first derivative of a one-variable function is zero at the points called stationary…

Q: 10. Find the particular antiderivative of the derivative f'(x) = 3x-1 – x-2 where f(1) = 5.

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Q: 5. What is the value of the second-order derivative of the function with parametric expression x =…

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Q: 9. Consider the interval [0, 2n] for the function y sec x. State an x- value at which the…

A: Given query is to find value of x for different conditions for instantaneous rate of change.

Q: 15 - What is the approximate derivative of f(x) = 5x³ + 4x² if we use f(ze+h)–f(za) forward…

A:

Q: 3- Suppose that the second derivative of the function y = f(x) is y" = (x + 1)(x - 2). For what…

A: 1)y'' = (x+1)(x-2)2)y' = (x-1)2(x-2)(x-4)

Q: 2. Determine the 8th derivative of y with respect to x of the function 1 f(x) = 1+x2 and find the…

A: Taylor series

Q: 1/3 Find the absolute extrema of the function f(x) = (x + 16) on the interval [-5,2]. Find the…

A: To find: Absolute extremum of the given function.

Q: (4)The instantaneous rate of change of f(r) = e- at a = 1 is . .. (5) The derivative of f(x) = sec2…

A: (4) We have So we get the instantaneous rate of change of the function at  as .

Q: 3 5.) y = ; x+5

A: Given:- y = 3/(x+5) y = 3(x+5)-1 Using Formula : [f(x)g(x)]' = f(x)g(x)' + g(x)f(x)' Now, y' =…

Q: 1.) Find the area under the curve y = x3 + 3x2 and the axis between x = 1 and x = 3.

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Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.

Q: Suppose x and y are functions of third variable t. In the equation *-+) , what are the values of the…

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Q: 4. The derivative of f(x) = ln x at x = 3 when hpresent = 0.001 and hprevious = 0.002. %3D 5. The…

A: f(x)=ln…

Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

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Q: 2.) Investigate the derivate of the function f(z)=Imz by using definiton of derivative.

A: The derivative of a function is represented as the change in variable with respect to change in…