1) Find the second derivative of f(x)= 24\x . (6) 2) If y = cos x, what is y (x)?

Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM 1. y Arctan- 3-V9-x2 2. y= 4 Arccos +…

A: 1.   From the given problem:   y=Arctanx3-9-x2   As we know:   d2ydx2=ddxdydx   So,…

Q: In y = 22 cosh1 2x

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Q: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…

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Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

Q: 4. Calculate the derivative of the given function directly from the definition of derivative y = v2x…

A: Given function is  y=√(2x+1)

Q: 17) Find the first derivative of f(x) = (cos4x)6 6 or f(x) = cos 4x

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Q: 1. Find the first derivative " if y = x sin 27x . dx

A: Given:  y=x sin 2πxTo determine the firstderivative.

Q: Determine the derivative of the following functions. 1. у 3 (8ӕ — 1) sinh(8a — 1) 2. y = (5)…

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Q: Find the derivative of y=cos4 x sin4 x Ans: 1/2 sin3 (2x) cos cos (2x) solution?

A: We simplify the given expression using the double angle property

Q: Find the derivative of f(x) = 2(x² + 3x) cos(sin(x³)).

A: I have used product re and derived of composition of two function

Q: 10. f(x) = cos (2x)e*²-1

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Q: What is the first derivative of q(x)= ln((7x^2+3x+7)/((x^5/6)(tan(x)))

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Q: 2 The derivative of (g(x))¯ is equal to (g '(x))¯. Select one: True False

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Q: Find the 46th derivative of y = cos (x) sin (a) cos (2) cos (x) - - sin (x)

A: Given y=cosx

Q: 4. Consider the function f(x) = 2 cos x x2 find its derivative

A: (4) Consider the given function. fx=2cosxx2 The quotient rule is defined as. fxgx'=f'g-g'fg2

Q: 2. In y = 2" + x cosh 2x

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Q: y = x* + 2 sin(x) + xº + 24*.

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Q: 4. If y = x cos x determine the 5th derivative. [y(5) = (60x – x³) sin x+ (15x² – 60) cos .x]

A: To find out the fifth derivative.

Q: if the derivative of x2sinx+2xcosx-sinx  is (Ax2+B)(cos(C(x/2))). FInd the value of A, B, and C.

A: Given: x2sinx+2xcosx-sinx Differentiate the equation.…

Q: 4. Find the first order derivative with respe. to x of the function u = In/x2 + y2 + z2 %3!

A: The function is u=lnx2+y2+z2

Q: Find the most general anti-derivative of f(x) = 9Vx +1+ cos x.

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Q: Find the derivative of the function. y = (( 1- cos 2x ) /( 1+ cos 2x ))4

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Q: Find the derivative of y with respect to x. -1 2х + 3 26) y = sec" 27) y = -sin-1 (5x2 + 2) 28) y =…

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Q: Find the derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

Q: 1 14) Use the definition of derivative to find dx 3- х.

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Q: Find the first derivative of: sin(x+y)+cos(x-y)=3

A: Given,           sinx+y+cosx+y=3 The objective is to find the first derivative.

Q: 3. Find the derivative of y = csc" (sec x), 0<x< 2n.

A: Given ddx(arccsc(sec(x))Let sec(x)=uWe know that ddx(cosec-1…

Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

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Q: Find the 3rd derivative of (1 + 2y)³ + eª (sin² y) - 3y cos(e=? )

A: Given data (1+2y)3+ex(sin2y-ycosex2=3y and find 3rd derivative or d3dx3=?

Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

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Q: The first derivative of y = sin( 4x + 3) is %3D а. - 4 cos(4x +3) b. 4 cos(4x +3) С. cos(4x+3) d. -…

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Q: Suppose x and y are variable (y is a function of x) that satisfy the equation Sin(x+y)=xy, What is…

A: To find the derivative of y with respect to x

Q: S Sin 5t-205 2t-2(03 2€ ; s(登)=

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Q: 15. What is the derivative of the function: F(x) = x cos(5x) F(x) = x cos(5x) F'(x) = (x)…

A: Solving

Q: Find the derivative of y: 1- y = (cos 0)V2 Cos O 2- y = 7sec ln 7 3- y = 2sin 3t

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Q: (b) Use implicit differentiation by partial derivative to solve for dx of the function 5x + xy 4y.

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Q: Find the derivative of y with respect to x. 2x + 3 26) y = sec-1

A: Let, z=(2x+3)/5   We differentiate using the chain rule

Q: Solve for the derivative of the function using chain rule. 8. f(x)= sin (2x)cos (3x)

A: Given problem:- Solve for the derivative of the function using chain rule.   8.     f(x)= sin…

Q: Solve for the derivative of the function using chain rule. 14. f(x)= 3lnx 15. f(x)= cos(cosx))

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Q: If f(x,y) is a real valued function of two variables then what is the second derivative of f?

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Q: Determine the first derivative of the ff. function a. y = 400(2)*+3 sin 3x b. y = Vxe2x cosx…

A: Given1) y=400(2)x+3sin3x2) y=xe2xcosx3)y=1+ln(3x2)1+ln(4x)We need to find the first derivative of…

Q: Which is the derivative of y= sin (x2-2x + 1)? О 2х-2) (2x-2)Cos(x²-2x + 1) O Option 2

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Q: Find the derivative of f ( x ) = 6 sin ^2 ⁡( x ) + 6 cos^2 ⁡( x ) at x = -6.5

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Q: How would you find the derivative of sin (z^6) + sin^6 (z) using the chain rule?

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Q: Find the fourth derivative of the given: (Show complete solution from first to  fourth derivative)…

A: The function is given by y = (2x+1)25

Q: 9) Find the value of the derivative at the point x=2 if f (x) = xv2x – 7

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Q: 8) Find the first derivative of f (x) = sin 2 (x3).

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Q: Solve for the first derivative of y = 3 sin x cos 3x

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