Find the second derivative of f (x) = 2 sin (3x). Enclose arguments of functions in parentheses. For example, sin (2æ). f" (z) =

Q: Find the derivative of the function f(x) = = sin(x) - 1 cos(2x) + 1 4

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Q: When f(0)=0 and f(pi)=0, what is the derivative of the function  7e^x + 6sin(x), and what is the…

A: Let the given function be:Applying the derivative with respect to x:Derivative of ex is ex and the…

Q: Find the second derivative for the functions defined as follows g(x) = 4x(ln x)

A: We have to find second derivative of the function: gx=4x lnx Since two function are in product so we…

Q: Find the derivative of y = cos"+8 (x).

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Q: 2. x² + 4xy + y² = 1

A: Differentiation

Q: Find the derivative. h(x) = In(cosh(7x)) h'(x) =

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Q: Find the first derivative of g(x) = - 9e* tan(x). : (x),6

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Q: Find the 80th derivative of y = cos(2x).

A: The given function is y=cos(2x)

Q: Find the derivative of 2 cos x 1. f(x) x+1

A: As we know that: The Power rule: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2 Given: fx=2cosxx+1

Q: Find the second derivative of the following  a .) 2x^3- 1/2x b.) Cos(x^2)

A: The given functions are  a) 2x3 - 1/(2x) b) cos(x2)

Q: Consider the function f (x) = sin β x,where β is a constant.   Verify that the function and its…

A: A function of the form p(q(x)) has its derivative by chain rule equal to p'(q(x))q'(x). For the…

Q: Find the second derivative of the function. f(x) = cos(2x?) f "(x) =

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Q: Find the derivative of the function y = sin '(- (5x + 4)).

A: Given query is to find the derivative of the expression.

Q: y = ln 1-x² 1+x²

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Q: Derive the formula for the derivative with respect to x of csc x.

A: We will write cscx= 1/sinx  Then we will use the quotient rule to differentiate

Q: 2х- 3 3. У3 5x +1

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Q: Use the first principles to find the derivative of cos(x -4x).

A: By the first principle  f'(x)=limh→0f(x+h)-f(x)h. So, dcosx2-4xdx=limh→0cosx+h2-4x+h-cosx2-4xh…

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

A: We have to find derivative

Q: Find the derivative of the function. y = sin-(9x + 1)

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Q: Find the second derivative for the functions defined as follows .p(x) = sin(x2)

A: We have to find second derivative of the function: px=sinx2 We know the formula of differentiation,…

Q: Find the derivative of cos-¹(sin x)

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Q: Find the 75th derivative of y=cos(2x)

A: Given function y=cos2x The 75th derivative has to be founded  first consider the smaller…

Q: Which of the following is the third derivative of y, if * y = (sinh 5)x2

A: we have to solve the problem

Q: Find the second derivative of f(x) * f(x) = cos² 7x

A: The given function is: fx=cos27x   As we know that; The Chain Rule: fgx'=f'gx·g'x The Product Rule:…

Q: Find the First Derivative of the Given Function: 2.) x=sec53t

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Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = π/4 , g'(2) = 5, and g"(2)…

A: singx

Q: Find the derivative of ,In sin-1) y = e %3D

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Q: Find the derivative of the function f(x) = 7x sin(4x).

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Q: Find the derivative of the function f(x) = at sin(7x + 14) + In(2r+10)

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Q: Determine the derivative of g ( x ) = 3 e-4 x*sin(7 x) with respect to x. = (x), 6

A: As per the guidelines, we need to author the 1st question.  We know that product rule is given by…

Q: 1+ cos x y = In 1-cos x

A: This question is based on chain rule differentiation.

Q: Find the derivative of the function. y = -4 sin 7x

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Q: Find the derivative: 1+ e2x = cos 1 - e6x f(x) f'(x) =

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Q: 5. y³ = 4(y + x²)

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Q: Find the first derivative of the function of f(x) using any method?

A: Given,

Q: Find the first And 2nd derivative  F(x)= e^x sin4x

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Q: Find the second derivative of the function f(x) = sin x2

A: Given f(x) = sin x2 To find d2f(x)dx2

Q: Find the second derivative of the function. f(x) = sin(9x?) f "(x)

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Q: Find the derivative of the inverse function at x=1 for the function y=sin(x−1)+x2.

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Q: Find the derivative of y with respect to x. y = In (tan -1 (9x5))

A: Given : y=lntan-19x5

Q: 3. y²(x + 2y) = 8

A: The Solution is dydx=-y2(x+3y)

Q: The 2nd derivative of the function x = Ci cosot + C2 sin ot with respect to t is

A: Given function is

Q: Find the second derivative, y" for the function cos(y) + sin(x) =1 by implicit differentiation. %3D

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Q: find the derivative of f(x)=(x^4+3x^2+8)cos

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Q: f(x) = (x + 6 sin x) (1 – 5 cos x -

A: To find the derivative of:f(x)=x+6sinx1-5cosx

Q: Find the derivative of y with respect to x. 58)y tan (In 2x)

A: Firstly, we use the result that  derivative of inverse of tan of x is 1/1+x^2

Q: Find the derivative of y with respect to x. y= In (tan (4x*))

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Q: What is the derivative of the function h(x) = ((4x^2-4)/(cos(x)))^8

A: We have to find the derivative of ((4x^2-4)/(cos(x)))^8 = 4^8(x^2-1) sec^8(x)= 65536(x^2-1)sec^8(x)