1. Let G(x) = | V³ +1dt. (a) Is the FTC II needed to calculate G(4)? (b) Is the FTC II needed to calculate Gʻ(4)?

Q: Show that is C is a function of x with derivative C'=C/x and N=C/x, the d/dx (C/x)=(C'-B)/x

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Q: A function is given as x - 6y = 5– x. Calculate the derivative of y with respect to r with two…

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Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

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Q: Q1) The dervative of the function f(x)= |x+2, using the definition of derivative is 1 b)- a) x+2 x+2

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Q: For what values of x does the graph of f(x)=2x^3+15x^2−36x−5 have a horizontal tangent line?

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Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 19 – x²;…

A: The given data is: gx=19-x2 To find the slope of the tangent line at the point 3,10.

Q: 4. Write the equation of the line tangent to f(x) = (e* +2x +1)In(e* +2x+1), when x = 0.

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Q: Find the indicated derivative dz/do for z= x^3+x^2/1-x-4x^2

A: We have to find derivative

Q: If f(x) = and g(x) = Vx, then the derivative of f(g(x)) is -VE (A) ( + 1) (B) -(x + 1)- -2x (C) ( +…

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Q: Compute the derivatives at the given value of a g(x)=(3x-5)/(x-2)     a=1

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Q: Find the critical points of the following function. f(x) = 5x? - 3x – 1 What is the derivative of…

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Q: 4. Use the linearization of the function f(x)%= at an appropriate x=a value to approximate 4.002

A: Given: The function f(x)=1x

Q: - Find the derivative o y with respect to n ort. 4 4 16

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Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: Find the slope of the line tangent to h(x) = f(x)g(x) at x = 6, given that the line tangent to the…

A: We have to find

Q: Given the function z=(x2+1)(x−1). Find the value of its derivative at x=−1.

A: The given function is z=x2+1x-1

Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

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Q: a) Calculate the derivative of f Cx) by first expanding and Simplifyıng the function fCx)=(2-3x) 2

A: Given,           fx=2-3x2

Q: Find the derivatives of the functions in Exercis

A: The given function is q=2r-r23.

Q: In (xv/x² + 7). n (xVx2 %3D · Find the derivative of the function y = In

A: To find the derivative of the Given function, we have to apply chain rule and product rule.

Q: 5 What is the derivative of5a2 + 10x + ? A None of the given choices B 10x + 10 + 3x2 10a4 + 10a³ –…

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Q: 5. Determine the area of the largest triangle that can be formed in the first quadrant by the…

A: The area is found by making a function of area into a variable and finding the values at which…

Q: Let f(x) = 4x3 + + 2Vx – 7. Find f'(x). 15. Find an equation for the tangent line to the graph of…

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Q: 2. For what values of x does the graph of f(x) = x³ + 3x² + x + 3 have a horizontal tangent line.

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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) = In x²;…

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Q: Find the actual error when the first derivative of f (x) = In x at x = 2 is approximated by the…

A: given  fx=lnx f'x≈fx+h+2fx-3fx-h4h to find the actual error

Q: Given g(x) = In(10x° + x), the derivative g (x) is %3D

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Q: Find the streamlines corresponding to: f(z) = z²

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Q: Find the indicated derivative.dp/dqfor p =q2 + 2/4q-2

A: Given a function in p in terms of q as shown below. We need to compute dp/dq.Here we use (u/v) rule…

Q: Find the first derivative for the following function. g(x) = 4e3x*+2x %3D A. g'(x) = 4e3x*+2x +…

A: Given function: gx=4e3x5+2x Differentiate the above function w.r.t 'x' g'x=ddx4e3x5+2x

Q: Let f=3x^2+2 and find the values below 1) f(x+h) 2) (f(x+h)-f(x)) 3) lim h→0 (f(x+h)−f(x))/h 4) Find…

A: The given function is f(x)=3x^2+2.

Q: Find the derivative of the function. x+6 g(x)=| x2 +4 5(4 – 12x +x?) ( 6+x (4 +x²) a. g'(x)= 4+x?…

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Q: For what value(s) of x does the graph of f(x)=10x^3 − 90x^2 + 240x +90 have a horizontal tangent?…

A: To find the slope of the tangent we find f'(x)

Q: Suppose 8 (x) 1+ x. What is the correct result of the derivative of g with respect to ? A 8'(x)=…

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Q: given that the graph of f(x) passes through the point (10,9) and the slope of its tangent line…

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Q: Suppose g(-2)=3 and g'(-2)=-4. Let f(x) = x3 + g(x). Find the equation of the line tangent to y =…

A: Given,     f(x)=x3+g(x)

Q: Suppose h(x): . What is the correct result of the derivative of h with respect to x? 3x · In (5)…

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Q: Find the function whose tangent line has the slope 3x² + 1 for each value of x and whose graph…

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Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

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Q: 1. Determine the third derivative of the following. A. f(x) = x³ – 4x² + 5x + 3 B. f(x) = Inx [ K:…

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Q: Q1) The dervative of the function f(x)= |x+2 using the definition of derivative is

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Q: Find the derivative of the given function 4. g(x) = (4 – 9x²)³ 3 5. h(x) x+5 = x2-9, 6. A(x) = v3x³…

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Q: find the indicated derivatives. dp/dq if p = q3/2

A: Given, p=q32

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: 1 4. Use the definition of the derivative to compute f'(x) given f(x) = 2x 3

A: Given,          The function is fx=12x-3 .

Q: Q4. Find the slope of the tangent line to the function f(x)= e* +3; x+2 at x=4 5x-10

A: Given : fx = ex5x-10

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 12 e* +…

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Q: The graph of f (x) = ax+b x²+3x-8 has horizontal tangent at (2, -1). Determine the values of a and…

A: Given query is to find the value of a and b.

Q: Derive the following formula for approximating the derivative f": 1 f"(x) ≈ (-f(x+2h) + 16f (x + h)…

A: Given: The formula is f'(x)≈112h -f(x+2h)+8f(x+h)-8f(x-h)+f(x-2h). To prove: The given formula. To…

Q: find the critical valves of f(x)= 3x?

A: We can find the critical values as below.