H.W • Find f (x) of f(x)= by using the definition of the derivative. • 1- Find if y=3r-4 and t = Vx +1. 2- Find 2 if y=: 2x-4 at x= dx 3x+3 3- Find if yv2 - VE

Q: 1. Find the derivative (dy/dx) of the following functions: a) xy = cot xy b) x cos(2x + 3y) = y sin…

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Q: 1. Find the derivative of the following functions. 1 (b) y(t) = Vi (c) y(t) = - (a) y(t) = t %3D

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Q: 1.2 s Find first derivative for the following functions. dx (a) y = 5+ 6x + 4x3 (b) y = In(2x) +x*…

A: Note:-Since you have asked multiple questions, we will solve the first question with three sub-parts…

Q: - 9x Find the derivative of y with respect to x if y = e dy %3D dx

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Q: Q2) Find the derivative of the function at Po in the direction of A. g(x, y) = x – (y/x) + V3 sec…

A: Let us consider the function z=f(x,y)  The derivative of the function at point P in the direction of…

Q: 1. determine the derivative with respect to time t of the following: a) 4x + 8y = 12 b) xy = 15 c)…

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Q: 1. Find the derivative d/dx using implicit differentiation of the following functions. Show your…

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Q: 25. What is the y' of y = tan(6x - 5)? a. y' 6csc2 (6x - 5) b. y' = tan(6) с. у' %3 6sec? (6х - 5)…

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Q: Ift=2cos (y² + 2), find the derivative of t with respect to y. A. 8y sin(y² + 2) cos(y² + 2) B. –8y…

A: The given function,  t=2cos2y2+2

Q: A. If r = r(t) represents the position function at time t of a certain particle, then what do you…

A: first derivative of position gives- velocity

Q: H.W: 1. find the derivative of the function f(x, y, z) = xy+ yz+ zx ,at the point P,(1,-1,2) in the…

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Q: 5. Calculate the following derivative x = 3e d y %3D Find (1) y=2e [y= 2e' ; dx? %3D dy 2) Let the…

A: (1) Given x=3e-t  and   y=2et The objective is to find d2ydx2. Now, dxdt=-3e-t and dydt=2et Then…

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

A: Given that

Q: 5. What is the derivative of the given function below? * x² + y² = xy dy dy dx dx Option, dy dx = =…

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Q: 19. The slope of the tangent to the curve (x2 + y²)² = 4.x²y at the point (1, 1) is 3 3 (a) - () – 1…

A: We have to find slope of the tangent to the curve x2+y22=4x2y at the point 1, 1. We know slope of…

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: We will use chain rule of partial derivative  If F is a function of  two independent variables x and…

Q: 4) a) Determine the derivative dx of the following functions y = 3** b) 1-3- 3e² 1² c) y d) y =…

A: We have to find the derivative.

Q: 4. Find all second order derivatives for the following functions. (a) f(x,y) = 2² + 3ry +2y², (b)…

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Q: 16. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is 3π 2 A.…

A: This is a basic application of derivative problem

Q: 1. Applying the definition of derivative, a. find dy/dx in each of the following: 1 a. 1] y = - x² –…

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Q: 1. Find the derivative of each given function with respect to x. (i) F(x) = | t dt 1+ t2' (ii) G(x)…

A: FUNDAMENTAL THEOREM CALCULUS If f(x) is continuous over the interval [a,b] and the function F(x) is…

Q: 22. Find the required derivatives. a) y = (4x3 - 2x + 1)-2; find y b) x = Vy? + 1;find x"

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Q: Q2: Find the derivative of f(z,x) = xe* + cos(2zx?) at a point (0,2,1)in the direction of V = i - 3j…

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Q: A. Determine the indicated derivative for each of the following functions. x3 cos y 1. Find fxzy for…

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want…

Q: Q. No. 5. Find the Derivative of the Given fur a) y= ev1n x( Inx) +2x b) f(x) = %3D a+x

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Q: Q1 / Find dy/dx by using the definition of derivatives for the following functions; -4 1. у %3D 2. f…

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Q: Find the derivative of y=2ecos.x)(sin(5x)) d'y Calculate as a function of t if x=t-t and y=t-t 2 dx?…

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Q: IV. Find the derivative of the given function. 1. u = t³(sin In t – cos ln t) 2. y = e-2* (1 + e-2x)

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Q: H.W: 1. find the derivative of the function f(x, y, z)= xy + yz + zx ,at the point P(1,-1,2) in the…

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Q: Find dy for the given values of x and Ax. 13 y= 4x" - 2x; x = -2; Ax= 0.3 What is the derivative of…

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Q: Q1)Find dy/dx for the implicitly defined relation sin(xy^2)=xarctan(y). Q2) Find the first two…

A: Given:sin(xy2)=xarctan(y)Differentiate both sides:cos(xy2)y2+2xyddx(y)=arctan(y)+xddx(y)y2+1Isolate…

Q: Vw Find the derivative of y = 3W with respect to w. dy dw

A: To find dy/dw

Q: II. Find by implicit differentiation. dx dy 1. 2x? + 2y? =17 2. x'y - xy = a'b 1_1, 3. x y 4. 2x +…

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Q: 1. Find the first derivative of y with respect to x (y') of the given functi 1. x³y-xy² +x² +y? = 0…

A: To find the first derivative of y using the given equation.

Q: 1 secz The derivative of the function y at z = 1 is equal to Select one: O a.-1 b. Does not exist…

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Q: + 1 (A) Find the derivative of y t3 – 1 (B) An object moves along the x-axis so that its position at…

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Q: 13. Find the derivative of the function T(z) = dz +b cz +d numbers such that ad – bc + 0. When is…

A: Hello. Since your question has multiple parts, we will solve first question that means question (13)…

Q: 9. Find the equation for the tangent line to f(x) = at A)9x+25 y=-34 B)9x+25 y =-24 r=-1 C)-9x+25y =…

A: Since you have asked multiple questions, we will solve the first question for you. If youwant any…

Q: d 1) Find sec dt t2 - 3t 2) Find the derivative of y t+1.

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Q: 1. Find the derivative (dy/dx) of the following functions: a) xy = cot xy b) x cos(2x + 3y) = y sin…

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Q: 3. Find the derivative of y with respect to x in the following functions : 18x'y (3x' – 2)' u? a) y=…

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Q: Q1: a) Find the directional derivative of S = In(2r +3y) at point (-1,1) in the direction of 4i -3i…

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Q: 2. Find the first and second derivatives of the following functions a) y = 6) y = e", c) y = In (sin…

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Q: (c) Use the chain rule to find the derivative of the function z = 2r*y³ – ry² along the curve given…

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Q: A. Find the derivative of the function at o P in the direction of A f(x, y) = x – E) V3sec-1(2xy)at…

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Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: Consider the curve F(x, y)=0. The objective is to show that if F has continuous second derivatives,…

Q: 2. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is A. 2y +…

A: Equation of tangent line through A(x1 , y1) is given by :- y – y1 = slope x (x – x1)

Q: b. Find first and second derivatives (dY/ dX, d'Y / dX² )of the following functions aX² +1 (а) Ү -…

A: The given problem is to find the first and second derivatives of the given following functions.

Q: 9. Find the equation for the tangent line to f(x) = at *=-1 A)9x+25 y =-34 B)9x+25 y=-24 C)-9x+25y…

A: Since you have asked multiple questions, we will solve the first question for you. If youwant any…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.