Product Rule Involving Trig Functions Consider the function p(t) = f(t)g(1) = (cos t+ sin t)t*. What is f'(t)?

Q: y =V V secxtanx; y 2

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Q: Direction: Find the first derivative of the following functions: 1. y = sin (2x) – cos (2x) 2. y =…

A: Solving question number 6

Q: Determine the following limits analytically.

A: Given that : The limits is limh→0 sin(x+h) - sin xh , where x is a constant .       i

Q: sin x+cosX Differentiate y = %3D sin x-cos x 2 А. 1-sin 2x -2 В. 1+sin 2x -2 С. 1-sin 2x 2 D. 1+sin…

A: Given,  y=(sinx+cosx)/(sinx-cosx)

Q: .f (x) = cos(-x) .f(x) = sin(8x) .f (x) = 2 sin(-5x) a) f'(x) = 2 sec(2x – 1) tan(2x – 1) %3D - b)…

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: Consider the function on the interval (0, 27). f(x) = x - 2 sin x (a) Find the open intervals on…

A: Given problem is :

Q: y = sec*0 – tan*0

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Q: sin z Find the derivative of the function g(x) = V1+ 2t dt using the Fundamental Theorem of…

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Q: Derivatives of functions with rational exponents Find dy/dx

A: Given, y=xx5+x To find dydx: Find ddxxx5+x: By Quotient Rule, dfxgx=g(x)·dfx-fx·dgxgx2…

Q: 1. y= sin (x² + 3x + 1)

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Q: 5. y = Arctan² (x³) '2х-1 6. y = Arccos 3x+1/

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Q: (c) Observe that the examples in (b) work nicely because of the derivatives you were asked to…

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Q: lim sin(x) x→0 xcos(x)

A: GIVEN : Limit

Q: implicit differentiation to find y from dy dx 3. use 3•X 3..x• siny - Sy = = le

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Q: f(x) = (- 3x_1 3

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Q: Consider the function on the interval (0, 27). F(x) = 1/2* + cos x (a) Find the open intervals on…

A: The given function f(x)=12+cos x on the interval 0, 2π

Q: Va +sin x lim- Va - sin x Do not use L'Hospital's Rule

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Q: 4. y = sec*e - tan*e

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: y=sin-1(x/x^2-1)x=3^1/2 find the equation of the tangent line

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Q: Tangent line given Determine the constants b and c such that the line tangent to f(x) = x 2 + bx + c…

A: Given: Equation of curve: f(x) = x2 + bx + c . Equation of tangent to this curve at x=1 is y=4x+2.

Q: Formula, Arc Length = | /1+ [f'(x)]² dx. Where f'(x) denotes the first derivative of f(x). Given the…

A: The formula for the arc length of a function f(x) bounded by the interval [a,b] is: Arc…

Q: sin(cosx * x + Vx) (cosx)2 sin (x²) * cos(x –-) sin(x) – 2

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Q: Using Secant Method find the 3rd iteration of the function f(x) = sin(x) + x^2 + e^x. using interval…

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Q: Using Secant Method find the root of f(x) = sin(x) + x^2 + e^x. using interval of [2 4] USE THREE…

A: This function does not have any root in interval [2,4]. Infact the function does notbhave any root…

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

A: To find the relative extrema of the function

Q: DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx, '2x-1 1. y = Arccos…

A: To find: The derivative of y=cos-12x-13x+1. Formula used: Chain rule of derivative: fgx'=f'gx·g'x…

Q: cosh“ x – sinh“ x = (cosh? x – sinh? x) (cosh² x + sinh² x)

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Q: f(x) .3 II

A: Given that function,     f(x)=5x3   f(x)=5x-3

Q: cos2x – sin2x cos2x For -F(x)+C. What is F(x)? cosx – sinx

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Q: sin 3x 4- lim sin Sx

A: Given query is to find the valueof the indicated limit.

Q: DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx, 1. y = sin (x? + 3x +…

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Q: Find the limit

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Q: Linear approximation Find the linear approximation to ƒ(x) = cosh x at a = ln 3 and then use it to…

A: Our Aim is to find the linear approximation to f(x) = cosh x at a= ln 3and then by carrying forward…

Q: integral using evaluate the substitution Sin(x) cos5lx) dx

A: Given,          ∫0π3sinxcos5xdx

Q: DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx, 3. y = tan vx2 – 1

A: Given: y=tanx2-1 To find: The derivative and  inverse of trigonometry function.

Q: *Implicit Differentiation Directions. Use implicit differentiation to find dy dx 1. x2-y2 8 %3D

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Q: bilowing function y = (sin-lx)sinx

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Q: 5. y = Arctan²(x³) 2х-1 6. y = Arccos 3x+1/

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Q: Using "Numerical Differentiation (Central Finite Difference)" Problem Solving f(x) = 4e-2xsin(x2)…

A: 1. The product rule for differentiation states that ddx[f(x)·g(x)]=g(x)f'(x)+f(x)g'(x), where f(x)…

Q: Let f(x, y) = x² + xsin(y). %3D

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Q: 1 2. Find the derivative of y =V1 - x2 +arcsin x 2°

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Q: y = cot(1+ cot(x))

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Q: Using the rule of sign evaluate e - वय x (a- Differentiation under Integral 1 +1 e-9x) dx x x

A: Note: In the question it has to be ∫0∞e-xxa - 1x + 1xe-ax dx, otherwise the question will not be…

Q: Implicit Differentiation. dy There is need to simplify. da Use implicit differentiation to find a.…

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Q: 1 f(x) = sin(x) – sin(3x) + sin(5x), [0, x] (a) Find the first and second derivatives of the…

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: 4. у"- Зу' + 2у cos e*

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Q: The Reciprocal Rule a. The Reciprocal Rule says that at any point where the function v(x) is…

A: Given: (a) The quotient rule is given as,

Q: 2. Determining Advanced Derivatives of Trigonometric Functions A. f(x) = sin x + cos x B. f(x) = sin…

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Q: QI Find f'(x) for 1+ sec-(x) S(x) 1- csc-1(x)

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Q: II sinx Find the slope of the tangent line to the graph of f(x)=: at x=- %3D cos x

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.