12. Find derivative of the following composite function using the Chain Rule: 2y t(y) = 6y² + 1+y? f(t) = 3t* + 8t, %3D

Q: 2. Calculate the derivative of the following y= (*- 3 + Sx) B. Ytan (x+ Se-2) (4x + 3) Tx-2) A. C.…

A:

Q: 4. Find the second derivative for the following functions : a) y=(x+!)' (ans.:6x +6+ 12) x' b)…

A: (a)

Q: Find derivatives of the following functions: y= (4x + 3)/In[2x* +3x -s] y= 3(e" +e*Xx² - 4)

A: ANSWER :

Q: Find the derivative of the function.

A: Given, To evaluate derivative

Q: Compute the following derivatives using the chain rule. g(y) = ln(1 + y).

A: Take 1+y = t  And use chain rule

Q: 2. Calculate the derivative of the following. B. Y= tan(x+ 5r-2) C. y=- (E +24) :(2-)

A:

Q: Find the third order derivative of y = In(cos(2x))³. A. y' = -40sec² (2x)tan(2x) B. y' = -80sec?…

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Q: OFind the second derivative of y = 4Vx + E + 10

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Q: 2. Calculate the derivative of the following. y = (x*- 3x2+5x) 3 y = tan (x2 + 5x - 2) А. B. (4x +…

A: Given  A. y=(x4-3x2+5x)3 B. y=tan2(x2+5x-2)C. y=(4x+3)3(x-2)2D. y=x2ex2-1

Q: Find the requested higher-order derivative for the given function. d3y of y = x" - sec(x) dx3

A: Given that y=x11-secx and we have to find third order derivative of y with respect to 'x' that is…

Q: 4- Calculate the second derivative of the function y = f (x) defined by the equation x3 + y3 +3xy +…

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Q: Use partial differentiation to find the derivative of the implicit function dy (3x'y-1)+ 7xy = 9…

A: We will use the given formula to solve this question.

Q: 8. Compute the derivative of the following equation. (1) y = (x +1)3(2x – 2)2 (ii) y2-4x² y+x=16

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Q: Find the derivatives of the following functions using CHAIN RULE. y=(5x + 1)2

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Q: 5. Use the chain rule to find the derivatives of (a) y = log; V4 + 1 (b) y = (x – e-")²

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Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x² + y²

A: Given,            f(x, y)=3xy2+2xy+x2ln1x2+y2

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

A:

Q: 20. Find the derivative of the function. y = 9cos(2x) a. y'=-18sin(2x) b. y' =18sin(2x) c.…

A: Option (a) is the correct option. Differentiate y using the chain rule.…

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: In (xv/x² + 7). n (xVx2 %3D · Find the derivative of the function y = In

A: To find the derivative of the Given function, we have to apply chain rule and product rule.

Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 – 7x³ + 21x² - i) y = (x² +…

A: As per guideline we have to solve first three subparts

Q: 4- Calculate the second derivative of the function y = f(x) defined by the equation x³ + y3 +3xy +…

A: The given function is: x3+y3+3xy+3y2+6x+6y=0

Q: = x³y² – 3x²y + 5x – 3y + 12

A:

Q: 27. The first derivative of y = is (4x+1) -24 b. 24 C. -6 6. (4x + 1)+ (4x + 1)+ (4x + 1)4 (4x + 1)*…

A: y=-2(4x+1)3

Q: Use the theorem of Leibniz in the following problems: 1. Obtain the n'th derivative of: x2y [x?y") +…

A: The objective of the question is determine the nth derivative of the given equation.

Q: If y = sin (4x - 5), then what is y' a. y = 4 cos (4x - 5) b. y 3 сos (4x - 5) C. y' = -cos (4x) d.…

A: In this question  we have to solve the given statements. NOTE: As per our policy we are suppose to…

Q: 1. Find the first derivative of y: y=x-6x³+2x²

A: Topic = Derivative As per guidelines , At  a time only one question can be answered. please repost…

Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

Q: If z = (x + y) e and x = 6t and y = 1 – t, find the following derivative using the chain rule. Enter…

A: In this question we have to find the differentiation of z with respect to t.

Q: Find the derivative of y with respect to t. y = t(In 1t)2

A: The given function,  y=t ln 1t2

Q: If z = (x + y) ev and x = 5t and y = 1 – t², find the following derivative using the chain rule.…

A: We are given that z=(x+y)ey,  x=5t, and y=1-t2. Now, we need to find dzdt.

Q: Calculate the derivative of the following function. y= sin (cos (3x)) If the Chain Rule only needs…

A: In the question we have to find derivative of the given function.

Q: If z=(x+y)e^y and x=7t and y=1−t^2, find the following derivative using the chain rule. Enter your…

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Q: Find the derivative of the function. r(x) = In| 4x + e* | Oa. 4+4e4* 4x +e*x O b. none of these…

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Q: If z = xy and x = e=' and y = sin(t), find the following derivative using the chain rule. Enter your…

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Q: Find Zxx=Zyy=Zxy=

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Q: If z = (x + y) e and x = 3t and y = 1 – t, find the following derivative using the chain rule. Enter…

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Q: dw B) Use the chain rule to find the derivative dt of w = x2 + y2 with x cost, y = sint.

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Q: 6. у3 In (x*+3х -1)2 V(5x+2) step1 step2

A: Derivative of function

Q: -7/2 = 8. Calculate the derivative of y with respect to , if x/2 + y dy dx

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Q: Find the third order derivative of y = In(cos(2x))". A. y' = -40sec²(2x)tan(2x) B. y' = -80sec…

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Q: Find the 1st and 2nd derivatives of the following profit function: =(xa-110)1/a that is, and find…

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Q: Find the derivative of the function: y = In e+2*+1 Oy = x"[(2x(ln x + 1) + 1] y = x*(2 + x + x² In…

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Q: (2) Find the derivative of the following: In xy = e*+y 4. %3D y = esint (In t² + 1) 5. y = In e 1+e…

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Q: 11. 5 4 Determine the derivative of y=x° – x* + 6. - Enter your next step here dy ab a + JT 00 () dx…

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Q: Q1)If f=x+y find second derivatives of fcx, fxy?

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Q: 9. The derivative of the graph x+y² D5 with respect to time is c-2y+ 20 C. a. y +x d. -y 2x +2y

A: Q 9 Given that: The graph: x2+y2=25

Q: et dt. · e2t 5. Find and simplify the derivative of f(x) = %3D 1 -2 In z

A: Assume g'(t) = e^t/(1-e^(2t))

Q: 2-х Find the derivative of y = Зx+1 -7 бх-5 6- А. (3х+1)2 В. (3x+1)2 7-6х С. (3x+1)2 D. (3x+1)2 Е.…

A: Proceed as shown below

Q: Determine the value of the derivative function for Ax) = (x + x)(x- 2) at x = 2. %3D A 6 в О с 5 D1

A: