2. UNIT 2.3: RULES OF DIFFERENTIATION Find the second derivative of the following functions: Simplify your answer. a. у %3D (2х3 + 5)6 5/244 x b. y == Vx sin (x) с. у 3 1+cos (x) d. f(x) = tan( 2x) e. f(t)=esint f. y=In(x+1) g. y= Arctan (e*)

Q: - a. Find the derivative of 3y – 2xy² = sin x + cot y b. Find the derivative of 2y x(3³) – In(²/²) =…

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Q: 3 The derivative of y = 3 cos (V1-x²) + (1-x²) 2 can be written as 3 (V1-x² sin ( /I-x² ) - (1-x² )…

A: Given : Function y is given and its derivative is also given To find: value of f(x) at x=0.43

Q: 9 tan t Find the derivative of the function y = 2 + 2 sect dy dt

A: Explanation and solutions is given below....

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Q: (x² +1)° {2x+1 V3x? +4 4. Use Logarithmic Differentiation to find the derivative dy / dx for y =-

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

A: Since we only answer up to 3 subparts, we'll answer the first 3. Please resubmit the question and…

Q: 13 Find the derivative of the function. Y = 2² + cos" (xx) a

A: Solution:- Given function is  y= a4+cos4(x)           ----------(1) Here, the variable is 'x' and…

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A: k = 1+2, 1-2explanation is given in below step

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Q: 2. Given x³+ y3 = 6xy dy? a. Use Implicit differentiation to find ? dx b. Find the equation of the…

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Q: Find the derivative of the following with complete solution A. y = sin x - 1 / cos x B. y = x^2 sin…

A: To Find the derivative of the following with complete solution

Q: 1) Find the second derivative of y = csc 2 e cot 2e %3D

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Q: B) Find the derivatives of the following functions: (for only 6) 5) y- In ( sin' 0) 6) y = log:() 7)…

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Q: 4.) Find the derivative of the following functions a.) y = sin(x) + cos(x) b.) y = csc(x)cot(x) c.)…

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Q: xe* (a) Use centered difference approximations to estimate the first and second derivatives of y √x²…

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Q: dy 1. FIND BY IMPLICIT DIFFERENTIATION: 9x = secy dx dy 2 a) FIND BY IMPLICIT DIFFERENTIATION: x4y³…

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

Q: 6) Find the derivative of the following functions 6.1) a(x) = x²(sin x)(cot x)e" 6.2) b(x) = ()-4

A: To find the derivative of the following functionsFormula:ddx(sin x)=cos xddx(cot x)=-csc2…

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Q: 3.8 Implicit Differentiation .) Use Implicit differentiation to determine dy 3 4 given the equation…

A: Given: x5+y3=5Differentiation formula:ddxxn=n.xn-1ddxc=0

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A: a. Compute the derivative using implicit conversion

Q: 4. Find the derivatives of the following functions: a) y² sin x – tan (x + y) + 3x = 0 b) y = x Inx

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Q: A2) Find the derivative of the following functions 2² + 4 (a). f(x) = 1² – 4 (b). f(x) = 2 tan '(x)…

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Q: X 3.9.29 Find the derivative of y with respect to t. y= sec

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Q: I need help with these questions. Please take me step by step

A: The given function is s(t) = –16t^2+96t.

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Q: -1 The derivative of the function y = sin Va at 1 is equal to 4

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

A: Firstly, we set cscx+cotx=u, then y=u^-1 and then we find derivatives  dy/du and du/dx

Q: dy 1. FIND BY IMPLICIT DIFFERENTIATION: 9x = secy dx 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ dx…

A: According to our policy at Bartleby, I can solve only one question. Given a function : 9x=sec y We…

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

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Q: 2. y = a Cos-1 (1 -2) + V2аx — х2 a

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Q: Suppose that x and y are related by the given equation and use implicit differentiation to determine…

A: →duvdx = udvdx + vdudx→dkdx = 0  where, 'k' is any constant.

Q: 1. Find dy/dx by implicit differentiation.  x sin(y) + y sin(x) = 7  y' = ?

A: Note:We are authorized to answer one question at a time, since you have not mentioned which question…

Q: 1.G(y) = (y − 1)4 / (y2 + 2y)7    a. G'(y) = ?

A: G(y)=(y-1)4(y2+2y)7 To find derivative we apply quotient rule uv'=u'v-v'uv2

Q: Given the function y = x(x + 1)3. Determine the value of its second derivative at x = 1.

A: Given the function  y=xx+13. We have to find the value of its second derivative at x=1.

Q: (a) Use the definition of the derivative to find the derivative of f(r) = V9- r. %3D (b) Find or y'…

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Q: (7) Suppose x4 + yª = 5 (a) Use implicit differentiation to find y' = . Simplify your answer. dy (b)…

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

A: Given:

Q: 18. Find an equation of the tangent line to the graph y = e * at the point (0,1). 7x dy if y = et…

A: As per guidelines incase of multiple questions asked, we are supposed to answer only the first three…

Q: Both x and ydenote functions of i that are related by the given equation. Use this equation and the…

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Q: 6. 7. 8. Determine the derivative of the curve with equation y = 4²x a) 4²x ln4 b) 42x In2 c) 4* In2…

A: We have to find out derivative

Q: 1. Calculate the derivative of the following function. y= V2x + 19 dx 2. Calculate the derivative of…

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Q: Find the derivative of y: 1- y = (cos 0)▼2

A: See the details solution in below

Q: 2. : Consider the function ry + cos y + x 2+ xy. (a) Find the derivative, dy/dx. (b) Find the…

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Q: 12. Given the function f(x) = Vx? + 12. %3D a) Find the gradient of the tangent to the curve at x =…

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Q: 1 y 4 18) Find the first derivative of y = -sin? x

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Q: (3) (a) Find dy/dx by implicit differentiation and evaluate the derivative at the given point tan (x…

A: a) The equation given is tan(x + y) = x The point is (0, 0) Differentiate both sides with respect to…

Q: The equation of a curve C is given by y3 + y = x* + a° + 8. (a) Using implicit differentiation, find…

A: Slope of thecurve at point P= Derivative of the function with respect to x computed at the point P…

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

A: Differentiating implicitly with respect to x on both sides. Solving left hand side first.

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

A: differentiate

Q: 1. f(1) = (9t + 7)2/3 %3D a. Find the derivative function of the function written above. b. Find the…

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