Given f (x) = 2x³ – 4x, fınd f'(6).

Q: Find the value of df-1/dx at x= f(a). f(x) = x² - 4x + 2; a = 5 1 O A. 6 1 O B. 14 1 OC. 10 O D. 6

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Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (E...

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Q: A bacteria culture initially contains 1500 bacteria and doubles every half hour. Find the size of th...

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Q: If f(x)=sin3xf(x)=sin3x, find f'(x)f′(x)   (answer) Find f'(2)f′(2) (answer)

A: Use the derivative formula, If, f(x)=sinax, thenf'(x)=ddxf(x)=acosax

Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line throug...

A: Given  Point : (8,-9,4) Vector : 1,5,-23

Q: dx + xP (y) = Q (y) dy Write the Linear DE of order one ydx + (3x - 2y+5) dy =0 in standard form

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Q: f(t)=6t^4-5t+7e^t. Then f'(t)=

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Q: Evaluate. d (x+5)

A: Derivative of differentiation variable is 1. Derivative of constant is 0.

Q: The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at æ = 5 and...

A: Given that: Leading coefficient =1At roots x=5 and x=0, multiplicity=2At root x=-5, multiplicity =-5

Q: What is the integrating factor of the linear DE of order one ydx + (3x - 2y +5) dy=0,

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Q: y=(2x2+5cos(x))7y=(2x2+5cos(x))7 Find dy/dx

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Q: Find the derivative of ƒ (x) = cos-1(In(4x²+1)).

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Q: 8. A 13-ft ladder is leaning against a house when its base starts to slide away (see accompanying fi...

A: Given figure: According to the given figure, with respect to angle θ. Hypotenuse=13 ftBase=12 ft An...

Q: Use the quotient rule to find the derivative of the following. 2x + 1 y = 2 +7 dy dx %3D

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Q: y=(6+e^x)^1/3 Find dy/dx dy/dx=

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Q: Evaluate. d 2 dx

A: Use the power rule of the derivative, ddx(xn)=nxn-1 And, the linear rule of the derivative, ddxay1±b...

Q: sec* 0 tan“ Od0

A: Using Substitution,

Q: se the definition to find the derivative of f(r)=∜r.

A: Given;      f(r) = r4

Q: -8x2 + 16x + 8 dx (x – 1)2(x² + 1)

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Q: cos s x dx 2. S: Vsin x

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Q: Upon multiplication by -3x" and using the substitution 2 = x3, dz = - 3x-4dx, the Bernoulli's DE -x ...

A: This question is based on Differential equation.

Q: Find y' if arctan (xy) = +x"y.

A: The solution is as

Q: (2xy + 2xy + 4x®)dx + (2xy + x*)dy = 0 (2y* + 2y* + 4x®y)dx + (2xy + xy)dy = 0 (2y* + 2y* + 4x*y)dx ...

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Q: differentiate g(x)=sinx cosx tanx

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Q: 4. Determine the point(s) at which the graph of f (x) = has a horizontal tangent. Simplify as much a...

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Q: Assume that a demand equation is given by g= 8000 - 100p. Find the marginal revenue for the given pr...

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Q: Evaluate the indefinite integral. | V4 + x2 dx = 2 ln +1 + 4 + 1 4 2

A: This question is based on indefinite Integral.

Q: Which of the following is an even function O f(x)= 3x^2 + 5x^3 + 10x^6 O f(x) = -7x^8 - 3x^4 + 5 O f...

A: We have to check the even functions from the given functions. 

Q: Determine whether the given differential equations are homogenous or not homogenous. If the equation...

A: A first order differential equation is homogenous if it can be writen in theform dydx=Fyx

Q: In exercises 1–24, differentiate each function. D f(x) = x*e* (2. F(x)= e2* cos 4.x 3. f(t) =t +2' 4...

A: Since you have posted multiple questions I can do first three subparts as per our company guidelines...

Q: Find the derivative of y with respect to x. 6х + 11 y = - csc 7 O A. 42 |6x + 11|V(6x + 11)2 – 49 O ...

A:     ddx(cosec-1x)=-1xx2-1

Q: dy The differential equation = 2y + 40 written in separable form is dy b. y+40 dy d. y+20 dy 40 2dx ...

A: on simplifying the given differential equation we will get the 

Q: 3. Use the chart below to evaluate the following values. Show as much work as possible! 4 -3 -1 -5 1...

A: By chain rule (f(g(x))'=f'(g(x))(g'(x) By quotient rule ddxf(x)g(x)=g(x)f'(x)-f(x)g'(x)g(x)2

Q: Question 4 The fuel efficiency of a car E(s), in miles per gallon, is a function of the speed of the...

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Q: 9. At what rate is soda being sucked out of a cylindrical glass that is 6 in. tall and has a radius ...

A: Volume of the cylinder ,V=πr2h ; where 'r' is the Radius and 'h' is depth of the cylinder.

Q: 1. Use L'Hopital's Rule to calculate the following limits: (a) lim,0+ xsim. (b) lim, 1- T/2-sin-1r V...

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Q: x+1 dx: VX -x

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Q: s(x) = In( vx³ – 1) е. f. k(t) = t²arctan5t

A: e) s(x)=lnx3-1f) k(t)=t2 arctan5t

Q: In Problems 13 and 14 construct an autonomous first-orde differential equation dy/dx = f(y) whose ph...

A: Here is the solution of the given problem. Phase Diagram of ODE

Q: Write the quadratic function in standard form. 9(x)=x+14x + 49 g(x) = Sketch its graph. grx) 10- -10...

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Q: Let y=(4x+2)^3 Find dy/dx dy/dx=

A: Given,             y = (4x + 2)³

Q: Using the substitutions Z = sin y and dz=cos y dy, the differential equation (3sin y - 5x)dx +2x² co...

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Q: V4 + x2 dx

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Q: For each of the series below select the letter from a to c that best applies and the letter from d t...

A: Here we have to find the correct option for the given series.

Q: Find y" if cos y + X =y

A: Given, cosy+x=y We have to find y''.  

Q: The order of the differential equat 2x2 - 3+y = 0 dy + y = 0 dx2 dx O not defined O 2

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Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dim...

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Q: (-1)" Consider the series Evaluate the the following limit. If it is infinite, type "infinity" or "i...

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Q: Use the quotient rule to find the derivative of the function. VE p(t) = 4t-3

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Q: 0.6 1 Calculate the integral o da. 1+z"

A: Given,           ∫00.611+x2dx