3. Evaluate the derivatives of the following: i. 2t +3 ii. x' sin x iii. In(3x-4) iv. (2x +5)"

Q: f(x) = acos(b\x) x2 COS

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Q: Find the derivative of y = cos"+8 (x).

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Q: 2. Find the derivatives of Y with respect to x if; x=arc sin ex.

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Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 1. у 3 ; d'y/dx

A: Question 1,Given,            y=x2-3x3xTo find : d3ydx3

Q: Find the derivatives of the functions defined as . y = -6x sin 2x

A: Given: y=-6xsin2x Now differentiate the given function, we get, dydx=ddx-6xsin2x⇒dydx=-6ddxxsin2x…

Q: Determine the derivative of the following functions. 1. у 3 (8ӕ — 1) sinh(8a — 1) 2. y = (5)…

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Q: Find the derivative of y with respect to x 3tan-1x + sin-1x = 4

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Q: f(x) = e2 sin¯+(3x) + In (cosh-1(e³x))

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Q: Find the Indicated Derivative for Higher-Order 1. y = 10x5 - 21x4 + 13x3 - 6x2 + 5x - 1000 ; y(6)…

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Q: What is the derivative of y=cos3(5x)

A: To find the derivative of: y=cos3(5x) For that use chain rule and ddx(xn)=nxn-1ddx(cos x)=-sin x

Q: What is the derivative of y = sin(3x²) cos(3x²)

A: We have to find the derivative of given function.

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

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Q: Which of the following is the third derivative of y, if * y = (sinh 5)x2

A: we have to solve the problem

Q: Calculate up to 2nd derivative the equation g(x) = -8sin (*+1) %3D

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Q: What is the derivative of * y = arctan(x2 + 1)?

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Q: Find the derivative of cos (ry) = -4x° y? + 5 using implicit differentiation.

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

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Q: Compute the derivative using derivative rules. y= cos(1/x) / (1 +x 2)

A: Derivative: The rate of change of a function with respect to a variable. y=fxy'=limh→∞ f(x+h)-f(x)h

Q: Q2) Apply the differentiation rules to find the derivatives of: Inx 5 (a) y=x*.e*+2- Inx- cosx (b)…

A: Solve the following

Q: Find the derivative of the function. y = 2 tan 5x

A: To find the derivative of: y=2tan5x Solution: y=2tan5x Differentiating both sides w.r.t x we get:…

Q: Determine the derivative of y=tan(cos-(4x)). -1 A y'=. 4XV1- 16x2 None of the given choices -1 y's…

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Q: 1 14) Use the definition of derivative to find dx 3- х.

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Q: Find the derivative of y given that y = In (sinh x) %3D

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Q: 2. y = x5 + 2x* + 5x3 + 4x² + x +1

A: Find the derivatives by applying basic differentiation rules.

Q: Find the derivative of the function

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Q: Can you help me step by step?

A: Given an equation

Q: Find the derivative of y with respect to x. -1 y = tan (In(2x))

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Q: 4. Find the first derivative of y = 170x tan (20x)+- In(49 – x 5e7-8cos

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Q: 2 Find the derivative of y = arctan(x´ + 3)

A: We have to find the derivative of the given function.

Q: Find the derivative of y = csc¯(In sin (x))

A: use simple integration formula.

Q: Q4/B By using implicit differentiation find dyidx for y 3x*+ cos.ry

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Q: What is the derivative of y = arctan(x² +1)?

A: Find the derivative of the function

Q: Find the derivatives of the functions defined as . y = cos4 x

A: Given function, y = cos4 x

Q: Find the derivatives of the functions defined as follows.

A: Given, y=-cos2x+cosπ6

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

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Q: Find the first derivatives of y = cos x tanx

A: Given: y=4cos x+1tan x

Q: Find the derivative of y with respect to x. y = 3 sin -1 (5x 3)

A: Given data:     The given expression is: y=3sin-1(5x3).   Assume 5x3=u and differentiate it with…

Q: 7) y=cos/2x+1

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Q: 1. Find the first order derivative of u = x*.

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Q: Find the derivative of y = /sin (7x + In(5x)) %3D

A: Here we have to find derivative of given function.

Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 2. Y= 2 Arccos (1-)+ v4x – x?

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Q: Find the derivative of y with respect to x. 6x + 7 -1 6. y3-Cos %3D

A: dydx=?

Q: 13 Find the secord derivative cy") y= x°+3x - when

A: see below the answer submit the q12 with what to do with the question

Q: I FIND THE SECOND DERIVATIVE(y") OF THE FF IN ITS SIMPLIFIED FORM 3x-4 1. Y= Arctan

A: To find second derivative of the given function.

Q: What is the derivative of the: y = (1 + cos2 x sin x2)3/2

A: Given: y=1+cos2x sinx232 differentiate with respect to x, dydx=ddx1+cos2x sinx232dydx=321+cos2x…

Q: Q2 find the derivative of the following: 1) y = 2stn (5x) 2) y = Inxn cosh 5x ,3) xsin14y = y tan-4x

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost other parts as…

Q: Find the derivative of y with respect to x. 58)y tan (In 2x)

A: Firstly, we use the result that  derivative of inverse of tan of x is 1/1+x^2

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: