6. Find the derivative of function. a) y = (x - 1)ā + 2x2-4x+7 b) y = cos* 3x * arcsin 3x2 |3D 3 c) y = + 3x3 X2 -

Q: 6. Use parametric differentiation to find if x= 212 +2, y=t* -7 dx Solution:

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Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

A:

Q: Find the derivative of O2 sec 2x O 2tan 2x O-2 cot2x O 1/cos2x y=In sin 2x

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

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

Q: 2. Find the third order derivative of y = In(secx + tan x). a. secx b. secx tan x c. - sec(x) + 2…

A: Explanation of the answer is as follows

Q: y3D(i+sinx)(I-sinl)!

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Q: 1. Find the derivative of f(x) = tan³(sinx) + %3D

A: The given function isf(x)=tan3(sinx)+x3+3x4

Q: Find the derivative of y with respect to x. 2x + 3 26) y = sec = sec-1 27) y = -sin-1 (5x2 + 2) 28)…

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

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Q: Find the derivative of f(2) = sinh(2²) – 2z cos(32). Is this an analytic functio %3D

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Q: Use Leibniz’s Rule to find the derivatives of the functions

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Q: Find the equation of the tangent line to the graph of f(x) = In(-x) at x = x0 = -e". %3D Equation:

A: To find the equation of the tangent line to the graph of: y=f(x)=ln(-x) at x=x0=-e4 The equation of…

Q: The derivative of sec2 2x(cos2x−sin2x) with respect to x is

A: Given: f(x)=sec2 2x(cos2x−sin2x)   Simplify the function before finding the derivative: By  the…

Q: Find an equation of the tangent line to y sin 2x = x cos 2y at the point π/2 , π/4 . Do not…

A: First we will find Differentiation of given equation to get slope of the tangent line. Now equation…

Q: Xyz. %3D Use implicit differentiation to find az/ar

A: The given function is ez=xyz.

Q: Calculate the derivative 23 d dz using Part 2 of the Fundamental Theorem of Calculus. 23 dt = dz -1

A: ddx∫-1x6t5-t23dt = ?

Q: In(5æ) Find the derivative with respect to x of y = %3D 5x y' = | %3D

A: Find the derivative

Q: 1. у %3D 4x? — Зх — 2.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Use implicit differentiation to find the derivative of: 9. х2 +x Arctany %3D у + 4…

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

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Q: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

Q: Find the fourth derivative of f (z) = 2" + In (x) – 160z. %3D Enclose arguments of functions in…

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Q: Is it true that the derivative of y=arcsin(cos2x) is -2?

A: The function is y=arcsincos2x.   Differentiate the function with respect to x.…

Q: Calculate the derivative. y = cos 3x In (cos ²3x) y' =D %3D

A: We can find the derivative as below.

Q: What is the equation of the tangent line to the function y = e-* - arcsin) x+1 2. at x= 0 ? A) y-…

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Q: Find the derivatives of the functions in Exercis

A: we have to find the derivative of the given function. g(t)=1+sin3t3-2t-1

Q: 1) Find the derivative of f(x) = 1+sin 2x %3D 2 cos3 x

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Q: Consider f(x) = 3 − cosx on the interval [0, 7]. When will the first derivative equal zero?

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Q: Calculate the derivative 33 dt da using Part 2 of the Fundamental Theorem of Calculus.

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Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) (2n 4+V3 2V3 At the…

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Q: Calculate the derivative d In (t)dt dx Ja4 using Part 2 of the Fundamental Theorem of Calculus.…

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Q: Evaluate the derivative of y = (2x – 1)° (x – 2)° at (1, -1). Use theorems of differentiation.

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Q: ex + siny = cos(x³y²) %3D

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Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: 23-4z2-2一4 y = %3D 1+ Va

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Q: Find sixth order derivative of the function f(x) = (x – 5)7.cos(5x) by using %3D Leibnitz theorem.

A: If y=uv where, u and v are functions of x then un and vn denote the nth derivative of u and v with…

Q: Use the Derivative Rule in Section 3.8, Theorem 3, to derive d 1 sec dx x. 지 V - 1 1지 > 1.

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Q: 2- Find the derivative of y with respect to the Exercises 1-3. = 6 sinh 1- 1 sinh (2x + 1) 2- In…

A: These are the hyperbolic function so use standard form of derivative of hyperbolic functions.

Q: Find the equation of the line tangent to f(x) = cos² x – sin²| %3D at x = 6

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Q: Use Leibniz’s Rule to find the derivatives of the functions

A: Given: y=∫x22x2lnt dt

Q: 2 12. f (x) = (1tsinx) Cosx

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Q: Use Leibniz’s Rule to find the derivatives of the functions

A: Use Leibniz’s Rule to find the derivatives of the functions

Q: s(w) = In( w - %3D

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Q: Find the derivative using the First Fundamental Theorem of Calculus. 13)음 V8t +7 dt dx

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Q: 2- Find the derivative of y with respect to the Exercises 1-3. y = 6sinh ; 1- = - sinh (2x + 1) y =…

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Q: 3. Write equation of the tangent line to the graph of the function f(x) = ecosx at one of the values…

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Q: 4 Find the derivative of f(x) using first principle %3D 3x2-3 of differentiation.

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.