y = csc (r² + t)

Q: Find the first and second derivatives of the functions in Exercises ( E q² +3 12q

A: We know that; The Power law: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The Quotient rule:…

Q: * Part 4: A derivative computation using the FTC and the chain rule d d (F(x*) dx dt dx

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Q: Use the Chain Rule to find the derivative. y = sin(x2)

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Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: y=57x3+1-3

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

A: Take 1+y = t  And use chain rule

Q: Use an appropriate form of the chain rule to find the derivative. R = e8s-t. = 4ø, t= ¢'/2 S dR dø…

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Q: Find the derivatives of the functions in Exercise

A: Given function is w=1z1.4+πz. To find the derivative of the functions.Solution: Power rule of…

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: The chain rule of two functions fx and gx is given by the following formula. ddxfg(x)=f'g(x)·g'(x)…

Q: use the Chain Rule to find the derivative. y = cos3(12θ)

A: Here given as y=cos312θ

Q: compute the derivatives indicated. f(x, y) = 3x²y – 6xyª, and ax2 ay2

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Q: Use the Chain Rule to find the derivative of the following functions.

A: To find the derivative of y=1-ex4 using the chain rule. Solution: Chain rule of differentiation…

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: Consider the function:  y=sin2x. Let u=2x  then  yu=sin u . Version two of chaon rule:…

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: We have to find the derivatives of the following function: y=sin 4x3+3x+1 We know the formula of…

Q: Find the derivatives of the functions in Exercise

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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: Find the third derivative. 1 (x + y)Z + (x – y)Z = a

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Q: Find all second order derivatives for z= 9y e TX. %3D

A: Solution of question as follow

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: Given function is y=sin4 cosz. To find the derivative of the given functions. Solution: Chain rule…

Q: 12. Find derivative of the following composite function using the Chain Rule: 2y t(y) = 6y² + 1+y?…

A: We have to find derivative

Q: Find the derivatives of the functions y = (3 + cos3 3x)-1/3

A: Given that, y=3+cos33x-13

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

A:

Q: Find the derivatives of the functions in Exercise

A: Given: y=x2+1x+5+1x Differentiating y with respect to x, dydx=ddxx2+1x+5+1x+ddxx+5+1xx2+1…

Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: Given- y=cos5t To use-  The Chain Rule to calculate the derivatives of the above function. Identity…

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: Find the first and second derivatives of the functions w = ez(z - 1)(z2 + 1)

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Q: Find the derivatives of y= s2-a2 / s2+a2

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Q: Use the Chain Rule to find the derivative. y = cos3(12θ)

A: Given function is y=cos312θ. To find the derivative of the given function using chain rule.…

Q: Find the first and second derivatives of the functions u =(x2 + x)(x2 - x + 1)/x4

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Q: Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

A: Given function y=cos4θ+sin4θ The version 2 of the chain rule is  dydx=ddxfgx       =f'gx·g'x Here…

Q: find the derivatives of the given function. g(x)= e2xln(x4)

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Q: Find the derivatives of the functions y = (x2 - 2x + 2)e5x/2

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Q: Use an appropriate form of the chain rule to find the derivative. R = e5s-t; s = 5¢, t = 6/2 %3D dR…

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Q: Find the derivatives of the functions y = xe-x + e3x

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Q: Find the derivatives of the functions y = 2e-x + e3x

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Q: Solve for the derivative of the given functions using the Chain Rule formula. Let f(x) = √(x2 + 3x +…

A: (a) fx=x2+3x+1 Inner function : u=x2+3x+1. Outer function : y=u.

Q: Calculate the first four derivatives of y = x- 1. Then find the pattern and determine a general…

A: We have the given function as y=x-1                ⋯⋯1 Now differentiating both of the side of…

Q: Find the first derivatives of y = x3 – x + 2 e*

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

A: Derivative of function

Q: Find the first derivative of the following implicit function: X² + 3xy + y² = 4

A: Given : x2+3xy+y2=4 Lets take first derivative  Take derivative with respect to x. apply the power…

Q: Calculate the derivative of y = /x+ If the Chain Rule only needs to be used once, which functions…

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Q: Find the first derivative of the following implicit function. x² + 3xy + y² = 4

A: Given : x2+3xy+y2 = 4

Q: Find the derivatives of the following using chain rule. c. f(x)= lnx^2 +4e^x d. y=axe^bx e.…

A: Given: c. fx=lnx2+4ex d. y=axebx e. y=e3x3-x2+5x-6 To find : Derivatives using chain rule. Formulas…

Q: find the following third derivative of y=(3x+2)2

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Q: y = (4x + 3)/ln[2x2 + 3x - 5] y = 3( e2x + e-2x )(x2 - 4

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Q: Use the Chain Rule to find the derivative. y = tan(θ + cos θ)

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Q: Find the derivatives of the functions y = 1/(x2 - 1) (x2 + x + 1)

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