A2) Find the derivative of the following functions 2² + 4 (a). f(x) = 1² – 4 (b). f(x) = 2 tan '(x) – 67 (c). f(x) = (x + 4 sin x) (1 – 3 cos ) tanz (d). g(x) = 4 - secr

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

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Q: 1. Find the derivative. g(x)=(4x-2)^5-√(x^2+8)

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

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A: The given inverse trigonometric function is,

Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

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Q: 4. Consider the function f(x) = 2 cos x x2 find its derivative

A: (4) Consider the given function. fx=2cosxx2 The quotient rule is defined as. fxgx'=f'g-g'fg2

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A:

Q: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

A: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

Q: 10) Find the second derivative of k(z) = 4 cscz.

A: Given: kz=4cosecz for finding second derivative of given function, we find first derivative then…

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A: We need to find derivative.

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Q: Can you help me with this problem step by step?

A: The given equation,

Q: 1) Find the derivative of the function 2 + X y = arctan V 2 – x .Simplify where possible.

A: Answer and explanation is given below..

Q: 1. Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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A:

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A: This question is based on chain rule differentiation.

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A: Given

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A: The detailed solution is as follows below:

Q: 22. Find the derivative of y = arcos(4x) with respect to x. - 4 4 - 4 - 4 В. 1-4x2 С. Vi-(4x) A. D.…

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A: In the question we have to find derivative of the given function.

Q: 5. Find the derivative of the following. 3x-5 а. у3 b. y = In (sin(3x-5)) c. y= e2x arc tan (2x + 3)…

A: Explanation of the answer is as follows

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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

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Q: find the derivative of y with respect to x, t, or θ, as appropriate.

A: On simplification, we get

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

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Q: 1) Find the derivative of the function: (3х — 1)3 Vx* — 1 f(x) = cos² x

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Q: Q. 2. a) Find nth order derivative of f(x) = In(2x-7). b) Find 3rd order derivative of y with…

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