Derivative formulas Derive the following derivative formulas given that (cosh x) = sinh x and - dx (sinh x) = cosh x. dx d (sech x) = -sechx tanh x dx

Q: Second derivatives Find y′′ for the following functions. y=xsin(x)

A: Here given function, y=xsin(x) and we have to find the second derivatives of the given function.…

Q: Derivatives by different methods Calculate the derivative of the following functions (i) using the…

A: Given:  Function y = x2 + 12x Concept Used: 1) The derivative of function ex is ex 2) Chain Rule of…

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

A: Given that a function.  And we have to find the slope at given point..  So for slope we have…

Q: Differentiation F(x) =cos[ ( root sin(tanaxl]

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Q: y = sec*0 – tan*0

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Q: y = Arctan?(x³)

A: We have to find dydx for y=arctan2x3.

Q: Derivative of y = |x| Graph the derivative of f(x) = |x|. Then graph y = (|x| – 0)/x - 0) = |x|/x.…

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Q: 1. y= sin (x² + 3x + 1)

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Q: 5. y = Arctan² (x³) '2х-1 6. y = Arccos 3x+1/

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Q: Calculating derivatives Find the derivative of the followingfunctions.

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Q: Derivative of the Square Root Function i) Find the derivative of for y = Vx for x > 0. ii) Find the…

A: We have to find the derivative of the given function.

Q: DERIVATIVE OF INVERSE FUNCTION. x + 2 Let f(x) 1- x • Show that the function is one to one 1 • Find…

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Q: 4. y = sec*e - tan*e

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: derivative of a(x) a(x)=sinx

A: Given query is to find 53 derivative of sin x.

Q: Differentiation. Find the value of the derivative of (iz + 6z2)° at 4i.

A: Let us define function f as                             f(z)= iz3+6z23

Q: f (x) = 8 sec(x) csc(x)

A: Here we will find the derivative,

Q: DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx, '2x-1 1. y = Arccos…

A: To find: The derivative of y=cos-12x-13x+1. Formula used: Chain rule of derivative: fgx'=f'gx·g'x…

Q: Va2 – x2 y = Arcsin-+ to

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Q: Derivatives of other trigonometric functions Verify the following derivative formulas using the…

A: The secant function in terms of cosine function can be written as sec x=1cos x. Tangent function can…

Q: Derivative of f(x) = sin(x) 2 For each x-value indicated, drag the purple dots up or down to…

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Q: Finding Tangent Line When Derivative Needs the Product Rule Determine an equation of the tangent…

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Q: First and second derivatives Find ƒ′(x) and ƒ″(x).

A: Given, To find f'(x)=? f''(x)=?

Q: Inconclusive tests Show that the Second Derivative Test is inconclusive when applied to the…

A: To show second derivative test is inconclusive.

Q: uous derivative. The table above gives values of fand its derivative for x=0 and x=4. If f (z) dz =…

A: Here we have ∫04f(x)dx=8 and  we have to calculate,  ∫04xf'(x)dx=?

Q: y = sech(x² + 2); y ||

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Q: DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx.

A: The above problem can be solved using chain rule. The chain rule states that for three functions f,…

Q: Derivatives Find the derivative of the following functions

A: The given function is y=lnx2-1, To find the derivative for given function , differentiate the…

Q: z +1 Q (2) = tan- (z)

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Q: DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx, 3. y = tan vx2 – 1

A: Given: y=tanx2-1 To find: The derivative and  inverse of trigonometry function.

Q: TC Find the SECOND derivative of the function f(x)=ln(tanx+secx) at x=- 3 Give EXACT value, No…

A: we are given the function,f(x)=In (tan x+sec x)

Q: 2. у%3D cos ? (2х — 1)

A: dy/dx = -2sin(4x-2)

Q: Equation of a tangent line. Ex. Given f(x)= 3x +4, find the equation of the tangent line at (-1,7)

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Q: 5. y = Arctan²(x³) 2х-1 6. y = Arccos 3x+1/

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Q: 3. y = cot(x + 2) cosh(x + 2)

A: Given: y=cot(x+2) cosh(x+2)                                  Here, cosh(x+2) is hyperbolic function…

Q: 3. y = tan vx2

A: Given that y=tanx2-1 find dydx

Q: Find the derivative of the function. y = cot2(sin(θ))

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Q: Verifying derivative formulas Verify the following derivativeformulas using the Quotient Rule.

A: we have to Verifying derivative formulas Verify the following derivativeformulas using the Quotient…

Q: Calculating derivatives Find the derivative of the followingfunctions. y = -x3cos x + 3x2 sin x + 6x…

A: Given function is  y=-x3cos x+3x2sin x+6xcos x-6sin x Differentiate y with respect to x.…

Q: 6. y = Arccos ()

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Q: sec x Let G(x) = Give an example of a value of x for which the line tangent to the graph of y = G(x)…

A: Given,            G(x) =sec x1 + tan x

Q: Calculating derivatives Find the derivative of the followingfunctions.

A: to find the derivative we will use the quotient rule which says  here v = 1+cos x and u = 1-cos x…

Q: y= Arctan

A: The function is y=Arctan2x3.

Q: sin Find the first derivative of 1-2 cos x

A: Given: sin(x)1-2cos(x)

Q: The Reciprocal Rule a. The Reciprocal Rule says that at any point where the function v(x) is…

A: Given: (a) The quotient rule is given as,

Q: DERIVATIVE OF TRIGONOMETRIC AND INVERSE TRIGONOMETRIC FUNCTIONS. Find dy/dx. y = cos2 (2x - 1)

A: The derivative of the given function can be determined using the chain rule.…

Q: Function      Point g(t) = −5 cos t + 1      (π, 6) Find the slope of the graph of the…

A: Given,