Find the derivatives of the functions in Exercis y = (1 + 2x)e-2x

Q: Find the derivative of y = 6e x – cosx.

A: Given function, y=6ex-cosx Used formulas, ddxcfx=cddxfx  c=constantddxex=exddxcosx=-sinx

Q: Find the derivative, dy/dx: y = x² In x3 ý =- 2 1-4 ln x x³ In? x 3. ý = -2 In x – 2x | y = --(- 3…

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Q: FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM 2. y = 2 Arccos (1-x/2)+ Square root of…

A: Second order derivative.

Q: find derivative of g(x)=integration3x2x (u2-1)/(u2+1) du

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Q: 3x-4 1. y = Arctan

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Q: Find the derivatives of the functions in Exercis y = xe-x + ex3

A: y=xe-x+ex3

Q: Find the first derivative of g(x) = - 9e* tan(x). : (x),6

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Q: Find the derivative of k(x) = log3(x) cos

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Q: Find the derivative. y= In x+3 %3D

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Q: Find the derivative of the function. 1 - e3x = cos y = cos 1 + e3x y' =

A: Differentiate

Q: y = In- e 2x+1

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Q: Find the derivative of the function. h(x) = x2 arctan(5x)

A: Given function: hx=x2tan-15x Differentiate the above function w.r.t "X" h'x=ddxx2tan-15x

Q: Shows the derivative function of: e3x+5

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Q: Find the derivative of y=. =x²- 1 2 COS X

A: Given,  y=x2-12cos x

Q: Find the second implicit derivative of the given using implicit differention y2-3x+2y=0

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Q: FInd the derivatives of the function f(x) from the first pribnciple  cos2x

A: Derivative from first principal is ratio of change in y to the very small chance in x.

Q: Find the derivative of the function. x + 6 X-6 y' = y = In

A: I have appended the formula used in the solution part of the question.

Q: 2х Find the second orfer derivatives of y=Tan" 1-x3

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Q: Find the derivative of the function. y = 2 cos5 x

A: Given, y = 2 cos5 x To evaluate, dydx

Q: Find the derivative of the function y = (1/2) arctan e2x

A: Given function is y=12tan-1e2x Chain rule of differentiation states that: ddxfgx=f'gxg'x And also we…

Q: Evaluate the derivative of y =e* sinh (2x). -3x

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Q: Find the derivative of function.

A: To fFnd:  Derivative of y=ln 4ln3x

Q: Find the derivative of the function. 1- e3x 1 + e3x y = cos y' =

A: Given that: y = cos1-e3x1+e3x To find: We have to find the derivative of the given function.

Q: Find the derivative of the function. y = (( 1- cos 2x ) /( 1+ cos 2x ))4

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Q: Find the derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

Q: 3. Find the derivative of y = csc" (sec x), 0<x< 2n.

A: Given ddx(arccsc(sec(x))Let sec(x)=uWe know that ddx(cosec-1…

Q: Find the derivative of the function. h(x) = x² arctan(8x) %3D

A: To find the derivative of hx=x2tan-18x

Q: Find the first derivative of y = 1 using the Chain Rule. (1– x4)6

A: These questions are related to differentiation, We will solve them using given information.

Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

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Q: Find the derivative of the function

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Q: Find the derivative of the function.

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Q: Find the derivative of the function h(x) = x2 arctan5x

A: The given function is h(x) = x2 arctan5x

Q: Find derivative of y=cos(7x).

A: The given function is

Q: Find the derivative of the function

A: We have to find the derivatives of the function: y=x tan-12x-14ln1+4x2 If two functions are in…

Q: Find the derivative of the function. InV y = In 6 - X %3D y' = %3D

A: Explanation of the answer is as follows

Q: Find the derivative of y with respect to s. y= sec -1(9s5 + 5)

A: To find the derivative of  y=sec-1(9s⁵+5)

Q: k(x) = x In x %3D

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Q: Find the derivative of y with respect to x if y = (5x2 – 10x + 10) e - 6x y' =

A: We have to find the derivative of y with respect to x.

Q: 4) Find the derivative of y = arctan(x² + 3)

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Q: find the first derivative in the form of dy/dx y=(3x-ln(x))^5

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Q: Find the derivative of the function.

A: Given

Q: 1 erivative of x²+2

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Q: Find the derivative of the function. 9 y =- Vx + 1

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Q: Compute the derivative for y= (e^-4x sin^2(x)) / (x^2 + 3x + 1)

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Q: What is the derivative of y = etan-1 2x 2

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Q: Find the derivative of f (x) =arcoth (e³" ).

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Q: 8. Find the derivative of y = In(3t) dt.

A: To Determine: Find the derivative of given integral:…

Q: Find the derivative of the function. h(x) = ets. - x + 1

A: Differentiate w.r.t x

Q: Find the derivative of y = arccos x + x 1-x²

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: