2) Find the derivative of the following func (c). f(x) = (x+ 7 sin z) (1 – 5 cos x) tanx (d). g(x) = 7- secz

Q: Q2/ A/ Show that the functions f(x) = sin-1() and g(x) = 2tan-Vx, have the same derivative. %3D

A: Given : f(x)= sin-1 ( x-1 / x+1 ) g(x) = 2 tan-1 (√x)

Q: Find the actual error when the first derivative of f(x) = sin(2x) at x = 1/8 is approximated by the…

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Q: 2. Find the derivative of a function at a certain number using the formula. f(x) – f(xo) f'(x) = lim…

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Q: 1 FIND THE DERIVATIVE OF EACH FUNCT'ON. 1.) y= sin () a.) y= Tan( 3x) 3.) y= Cos( 3

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the derivative of the function.

A:

Q: 2. x² + 4xy + y² = 1

A: Differentiation

Q: 7. Find the derivatives of y = cos- (sin(2x)) (show work)

A: Using derivatives of composite function. Or Using trigonometric transformation.

Q: 5. Calculate the derivative of the following functions. DO NOT SIMPLIFY a. f(x) = x³ (arctan(x²) –…

A:

Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: 1) Find the derivative of the given function with respects to e 3 tan 6 In 3 y

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Q: • Show that both of the functions f(x) = (x − 1)^4 and g(x) = x^3 −3x^2 + 3x+ 2 have stationary…

A: given functions fx=x-14gx=x3-3x2+3x+2 (A) to show both have stationary point at x=1 differentiate…

Q: 1. Explain how to use the differentiation part of the Fundamental Theorem of Calculus px 2+sin(4t)…

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Q: Find the second derivative of the following  a .) 2x^3- 1/2x b.) Cos(x^2)

A: The given functions are  a) 2x3 - 1/(2x) b) cos(x2)

Q: 5a) Using the formula man = lim+)=/G2 determine the derivative/ slope of tangent for h→0 the given…

A:

Q: 4. Find the derivatives with respect to x of the function 2 – 3x^2. 5. Differentiate ax² + b to the…

A: Using derivative of composite function.

Q: Find the derivative of the following. y = -1/3tan3 x - sin2(2x)/tan x - cos2(2x) cot x +4

A: Differentiation of the function can be found with the help of the differentiation formula.…

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: a. h(x) = X-…

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Q: 10 Find the derivative f'(0) of f(x) = at x + 4 x = 0 using the laws of differentiation.

A: Derivative of the function

Q: 2. Find the derivative of the following functions: (5x+ 1)'(x + 3)5 cos°(x) sin°(x) (a.) f(x) = .…

A: Given f(x)=5x+77x2+35cos2x sin3x3   As per our guidelines we are supposed to answer only first…

Q: The derivative of f(x) with respect to x is the function f'(x) and is defined as f'(x) = lim 0…

A: To find f(x+h) replace x by x+h in f(x).

Q: e. f. f(x) = cot(-) X f(x) = sin(x³ - x)

A:

Q: 2) Find the first derivative: a) y = cot * (3x² +7)

A: Differentiate wrt x

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Use the basic definition of Cosh to find the derivative of the function, Coshx=ex+e-x2. Find the…

Q: 2. Let f(x) = /1 – x² . Find f(8) (0), i.e., the eighth derivative of ƒ evaluated at the point 0.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the second derivative of f (x) = 2 sin (3x). Enclose arguments of functions in parentheses. For…

A: Differentiate two times

Q: 4) a) Determine the simplified expression for the 623rd derivative for the function f(x) =cos(2x)…

A: a)   fx=cos2x+sin2π     =cos2x+0      = cos2x

Q: 12. The derivative of cos(1 – x) with respect to x is ;A. - sin(1 – x) B sin(1 – x) C -(1– x) sin(1–…

A: Given that: Let f(x)=cos(1-x)

Q: The derivative of the function f is defined by ƒ'(x) = (x² + 5) cos (3x). What is the x-coordinate…

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Q: Find the derivative of the function f(x) = at sin(7x + 14) + In(2r+10)

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Q: 11. Use the limit definition to find the derivative of f(x) = x² -2 x. 12. Find an equation of the…

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Q: Solve for the derivative of the following trigonometric functions. 1. f(x) = e3x 2. f(x) = x³ ex 3.…

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Q: 6. Find the derivative of the following (express answer in simplest form): 1+ sinx a. f(x) = In…

A: Topic = Derivative

Q: 4. Find the derivative of the following function. 1+ sinx g(x) = - V1+ cos x

A: Given: gx=1+sinx1+cosx for finding derivative of given function, first we simplify given expression…

Q: Find the second derivative of f (x) = 9 sin (2æ). Enclose arguments of functions in parentheses. For…

A: Second derivative of f(x) is given below...

Q: Find the derivative of the function: f(x) = [sin(4x + x)] [cos(x4 + 4)] f(x) = e3x²+*(cscx + secx)2…

A:

Q: 2. Find the derivative of y = tan°(/1 – x²). Make any obvious simplifications. %3D

A: Using chain rule of differentiation.

Q: Solve for the derivative of the given functions using the Chain Rule formula. a.) Let f(x) = √(x2 +…

A: Solution

Q: f(x) = 2 cos I - 3:

A: Of a function y = f(x) of a variable x is a measure of the rate at which the value y of the function…

Q: 7. Consider the function f(x) X - 3 a. Using the definition of the derivative at a point, calculate…

A: Given : f(x) = x / x - 3   (1) f' (2)  (2) tangent line when x = 2 (3) normal line when x = 2

Q: f(x) = sin (x³)

A:

Q: 1. Explain how to use the differentiation part of the Fundamental Theorem of Calculus to determine…

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Q: 29. Prove the following derivatives by using the definition of derivative. (a) (") = n. dx nxn-1

A: topic - derivative and limits

Q: How do I find the 20th derivative of f(x)=(2cos x)(cos 3x)? I think there must be some trick because…

A: Given:

Q: 2. Determine the 8th derivative of y with respect to x of the function 1 f(x) = 1+x2 and find the…

A: Taylor series

Q: Use the theorems on derivatives to find the derivative of the following function:   y = (cos(x))2 +…

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Q: Find the derivative of the given function 1+ sin(3 f(x) = ( V + 1

A: To find the derivative of the given function  Use formula of  Derivative of u/v  = { u'v - u v' } /…

Q: 1. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 7. Use the limit definition of the derivative to find f'(x). Then find the equation of the tangent…

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Q: What is the derivative of the function h(x) = ((4x^2-4)/(cos(x)))^8

A: We have to find the derivative of ((4x^2-4)/(cos(x)))^8 = 4^8(x^2-1) sec^8(x)= 65536(x^2-1)sec^8(x)