Question 7 Apply the first principle of differentiation to find the derivative of ( a) f(x) = Vi-2x f(x) =- x-1 (b) 7 (c) f(x) = sin 2x

Q: Find the derivative of h(x) tan 3x+cot 3x

A: Solving the problem by finding the derivative of the function.

Q: Find derivative of the following functions 1. y= sin^-1 2x^2 2. y= tan^-1 2x^2/5

A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

Q: Find the derivative of (b) f(x) = 2 tan-1(x) – 7x

A: Givenf(x)= 2 tan-1(x)-7x

Q: When f(0)=0 and f(pi)=0, what is the derivative of the function  7e^x + 6sin(x), and what is the…

A: Let the given function be:Applying the derivative with respect to x:Derivative of ex is ex and the…

Q: Find the derivative of the inverse of the following function at the specified point on the graph of…

A: Consider the given function  fx=sinx

Q: Find the derivative of the function.

A:

Q: 34. f(x) = er+2)

A: Solving using chain rule of differentiation.

Q: Question 7 Use the chain rule to find the derivative of f(x) = 6V6x° + 7x Type your answer without…

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Q: -y = sin-1 (x), y €|-5 (х), у € 2'2

A: topic - proof of inverse trigonometric function

Q: Example 1: Use differentiation rules to find the derivative of the following. Express your answer in…

A:

Q: 2. Use rules of differentiation to find the derivative of the function 5a° (x- +3) g(x) = x2 +1 Show…

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Q: Find the derivative of the function. f(x) = ln   x + 2 x − 2

A: Given,            fx=lnx+2x-2

Q: 4. Find the derivative of the following function. 1+ sin x 8(x) = 1+ cos x

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Q: Find the derivative of cos-¹(sin x)

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Q: The equation of a curve is given by f(x) = √2x-1. a) Use the definition of derivative to find f'(x).…

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Q: 2. Find the derivative of g(x) = 2x sin x.

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Q: Find the derivative.

A: Given     y=sin-1xcos-1xdydx=cos-1x ddx sin-1x-sin-1x ddx cos-1x ( cos-1x  )2       =cos-1x 11-x2…

Q: Find the derivative of ?(?) = √? sin ? by using the Product Rule. Simplify your answer, if possible.…

A: Derivative of function

Q: Question 9(both parts)

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Q: cos (5x-0.1) w(x) =- e*

A:

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: Given, f'(x)= sec22x; π2, 0

Q: f (x) = cos-(sin(x² + 3х))

A:

Q: 28. f(x) = arctan /x

A:

Q: (a) Find the derivative of the function g(x) = sin2 x + cos2 x (b) then use a trigonometric…

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Q: Find the derivative of the function. "1(* - VI + x) y = 9 tan

A: derivative

Q: Find the derivative of the function. y = -4 sin 7x

A:

Q: Find the 73rd derivative of the function f(x) = 2 sin(x). f (73) (x)

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Q: Question 13 Find the second derivative of f(x) = x 3Inx O x(5+Inx) O 5x + Inx2 O x(5+Inx2) O 2x…

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Q: Solve the second derivative ду? for f(x) = tan-1

A: the given function f(x)=tan-1x2y2to find ∂2f∂y2

Q: Find the derivative of the function. Simplify where possible. y   = Cos-1(Sin-1t)

A: y=cos-1sin-1t

Q: The derivative of y=sin^{5}x

A: Differentiate using the chain rule dy/dx= dy/du * du/dx

Q: Question 10 Calculate the second derivative of the function y= In(cosx). -csc2x -sec?x c) cscx D)…

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Q: Find the derivative of the function. y = sin-1(4x + 1) У'%3

A:

Q: Find derivative of the f(x) = sin-1*- 1 x+1 function

A: To find the derivative of the function

Q: f(x) = sin (x³)

A:

Q: x' Find the derivative of h(x) sin x 4x2+2

A:

Q: EXAMPLE 1.2 The Derivative of the Log of an Absolute Value For any x for which tanx # 0, evaluate In…

A: Solution of the problem as follows

Q: Solve for the derivative of the Inverse Trigonometric Differentiation.  1.  g(x) = 3 tan -1 (3x)…

A:

Q: What is the derivative of f(x) = (tan^-1)((3+x)/(1-3x))

A: Given:f(x)=(x+3)arctan(x)1-3xf'(x)=ddx(x+3)arctan(x)1-3x=ddx(x+3)arctan(x)·(1-3x)-(x+3)arctan(x)·ddx…

Q: Find the derivative of each function 2 sin x 5x3 1. h(x) = In x -3e* h(x) = 2 cos x g(x) : 1+7x

A:

Q: Find the derivative of  f(x) = tan(cos(x^2))

A: f'(x) = d (tan(cos x2)dx  f'(x) = sec2(cos(x2))d cos x2dx               because   d (tan(x))dx =…

Q: 3. Find derivative 4 =xe?

A:

Q: 1+sin 2 x Find the derivative of f(x) 2 cos3 x

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Q: Example: Find the derivative of each function. (a) ƒ (x) = (4æ³ – 5æ)' 3 - (b) g (x) = e2a.cot x (c)…

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Q: Question 7- Find the derivative. g(x) = /9 - 6x +x²

A: According to the guidelines in case of multiple questions we are only allowed to do first question,…

Q: C. Find the derivative of each function. x' - 2x 3. h(x) = 4. F(x)= sinx- cosx-tan x tan x

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find the first derivative of the function y = In[tan (pi/4 + x/2)

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Q: The second derivative of the given function is - 5 sin (2 - 5x)

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Q: Question 12 Find the 2nd derivative (y") of y=√x ln x In 2

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Q: How are the derivatives of sin-1 x and cos-1 x related?

A: Given functions are sin-1x and cos-1x

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: