Q1: Find the value of the constant K if the function 4-x is continuous at x=2. f(x) ={3- Vx +5 [K ;x = 2] Q2: Find the derivative of: (1) y = sin(x² + vx, 2 (2) y= 3x – 5x² +10 1+ sin x (3) y = tan 1- sin x

Q: f'(x) (11 + x)2 -V11,V11 VIī, VIT EX =p 7 of 7 2x(x² – (11 + x2)3 Substitute x = -/11, 11 in the…

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Q: 3. Suppose the function f has second derivative f"(x) = x2(x – 3)(x+2)*(? – 1). = T- (a) How many…

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Q: If the derivative of the function f (x) is f'(x) = 18z2 + 2x + cos(z) + 6, then which if any of the…

A: Solve the first order differential equation by separation of variable and integration.

Q: 4. Compute the derivative: y = 2+ cos x 5. Determine the equation of the line tangent to y = V1 + x3…

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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

Q: 1. Find the first derivative of y with respect to x (y') of the given function 1. x'y-xy? +x? +y? =…

A: As per guidelines we have to solve one question

Q: Q3: i) Find the derivative of the function of y = (x² + 1)sin 3x %3D (ii) Find the absolute maximum…

A: Given:  i) y = x2 + 1sin3x ii) f(x) = x2-13, -3≤x≤3

Q: 1) Use forward and backward difference approximations with error of O(h²) and a centered difference…

A: As per the question we are given the following function : f(x) = x2e-3x/7 And we have to find the…

Q: 1. Find the derivative of the following using implicit differentiation. BARZA c. y = sec(x + y) TYON…

A: The implicit function is of the form f(x,y)=0 in implicit differentiation y is a derivative of dydx…

Q: 4)Given f(x) = 2x/(x2 + 1) a)Find the derivative. b)Find the critical numbers .

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Q: c) If f'(x) =3+ 4x and the curve f(x) passes through the point (1, 8) i) Find f(x) ii) Find the…

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Q: 1) Use forward and backward difference approximations with error of O(h²) and a centered difference…

A: Given function  fx = x2 e-3x7 Step size h =0.2

Q: 10. Iff(x) = Vx find f (4). 11. Use the limit definition to find the derivative of f(x) = x² –2 x.…

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Q: Q4: Find the derivative of the function at P, in the direction of A 2 1) f(x, y) = 2xy-3y², P.…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 1. Find a, b, and c such that the function f(x) has a derivative at x=0 and x=2, where: tan-1(x);x…

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Q: Consider a function y =f(t) with domain (0. 1, 4. 2). Use the graph of the derivative function,…

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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: What is the first derivative of f (x) = ln n A)? 3x²+7x 5х Select the correct answer below: бх-7 O…

A: Given query is to find the derivative of the expression.

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: а. h(x) —…

A: We need to find derivative.

Q: -1 Find the derivative of the function: y=6 sin ¹¹ (x²). y'= y'= O y'= 12x y'= -X 2x 2 + X 12x 4 4 X…

A: Given y =6 sin-1 (x2 )

Q: х+1 3.) y = х-2

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Q: 3. The slope of the tangent line to f(x) = A tan(¤) is 1/2 when z = 2n/3. Deter- mine the equation…

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Q: 3. Find the derivative of y with respect to x in the following functions : 18x'y (ans.: (3x-2) a)…

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Q: Match each function with its derivative. Y • x² x4 + 5x 1. cos x - - x8 8. sin x + x4 3x x4 -1.…

A: Concept: Differentiation of xm dydx=xm=mxm-1 dydx=ax=loge(a)· ax

Q: If f(x) is odd function, then the derivative of y =sinh (-x)) equals Select one: f'(x) O y'=- V…

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Q: 1. Find the derivative of the following functions. (find y') a. у %3DIn(cos(20)) b. cos(xy) = x - y…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: 3- Show that this function is differentiable for all and find its derivative f(2) = f(x+jy) x - 15x…

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

A: The function fx=ln2x-7. The first derivative of the function fx=ln2x-7 is computed as follows,…

Q: . Use Euler's method with a step of 0.1 to estimate f(2.5) if f(1)=-2 and the derivative of the…

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Q: Let f (x) =x. cos(x2). what is the correct result of the derivative of f with respect to x? A…

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Q: If f(x,y)=3 sin (2x+y)-4 cos (x-y) then the second derivative f , is a. 3 sin (2x+y)+ 4 cos (x-y) b.…

A: In the question it is asked to calculate the double derivative of the function given.

Q: A2) Find the derivative of the following functions 1² + 3 z² – 3 (a). f(x) : (b). f(x) = 2 tan (x) –…

A: As per bartleby guidelines, we are supposed to solve only first three subparts if multiple subparts…

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

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

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Q: 2. Find the equation of the tangent line and normal line to the curve f(x)= 3x at the point(1,1). x²…

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Q: x2 1)Calculate the derivative using FTC(1): g(x) = ʃ  (t5 − 9t3 )dt…

A: 1) to find the derivative of the integral using FTC(1)

Q: 10. Consider the function f(x, y) = 4 + x* + 3y* a. Show that the Second Derivative Test is…

A: (a) Calculate the value for second partial derivatives w.r.t x and y.…

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: e sin x…

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Q: 3 x° In x x° with respect to X - Find the derivative of y a) 6x - a2 b) None of these c) p6 ln x x2…

A: Given query is to find the derivative of the expression.

Q: 3 Find the derivative of the following functions. (Answer five only) 1-r = 120-1 - 40-3 +0-4 2- y…

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Q: 5- When the first derivative of the y = sinx function at x =pi/4 is calculated with the forward…

A: We will use basics of numerical methods here

Q: Example3: a) Find the derivative of f(x.r.:)= r - -: : at P(1.1.0) in the direction of 1= 2i-3j-6k.

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Q: 7. Find the second derivative given g(x) = sin x² A. 2(cos x? – x sin x?) B. 2(cos x? – 2x² sin x²)…

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Q: d 1 (a) Prove that (sin- x) dx V1 – x² (b) Find the slope of the normal line to the graph of the…

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

Q: The equation of the tangent line for the graph of F(x)= Ln (f+4)df at x=2 is O y-Ln(68)(x-2) O…

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Q: 1.) Find the area under the curve y = x3 + 3x2 and the axis between x = 1 and x = 3.

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Q: 5. Let f(x) = |cosx),x € (0,21). Determine that where the function S is differentiable, and where it…

A: Since not a particular question asked as per guidelines solution to only first question (i.e Q5) is…

Q: 4x Q No.2. a) Evaluate the derivative of the function: F(x) = Seova (In t) dt. b) Find the…

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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…