1 FIND THE DERIVATIVE OF EACH FUNCT'ON. 1.) y= sin () a.) y= Tan( 3x) 3.) y= Cos( 3

Q: (1)Let f(x)=x -7x+15. Find the derivative, f'(x) using the definition of derivative. Also find the…

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Q: Find derivative of the following functions 1. y= sin^-1 2x^2 2. y= tan^-1 2x^2/5

A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

Q: Find the derivative of f (x) = -6 tan (x). Enclose arguments of functions in parentheses. For…

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Q: 7. Find the derivatives of y = cos- (sin(2x)) (show work)

A: Using derivatives of composite function. Or Using trigonometric transformation.

Q: 2. Find the derivative. Simplify where possible. (b) у %3 tanh-1(г3)

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Q: 10. Find the derivative of y = cos /sin(tan 7x)

A: We will find the derivative using Chain rule

Q: Find the derivative of the function y = cot^-1 x^2– cos^-1 (x + 1/x – 2). %3D

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Q: compute the derivative y = sin(2x) cos2 x

A: Given y=sin(2x)cos2x The product rule of derivative is given by:

Q: +0.0001) – 1, tan(4 4. Which derivative is approximated by 0.0001

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Q: 3- Find the derivative of sinx +x /2+cos x.

A: The given function is fx=sinx+x2+cosx. The formula for differentiation for the sum of functions is…

Q: Find the derivative of the following. y = -1/3tan3 x - sin2(2x)/tan x - cos2(2x) cot x +4

A: Differentiation of the function can be found with the help of the differentiation formula.…

Q: We cannot find the derivative of composed functions. We can however, using some algebra, find the…

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Q: Compute the derivative of the function y = 7 sin-(x) at the point x 3 (Use symbolic notation and…

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Q: Compute the derivative of the function y = 7 sin¬'(x) at the point x = (Use symbolic notation and…

A: A detailed solution is given below

Q: 3x-4 1. Y= Arctan 4

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Q: Find the indicated nth derivative of the following: 1 7. 2nd derivative of y = xArcsinx + v1 – x²…

A: Find derivative using product rule and composition of functions rule

Q: 11 In(x)sin (x²). Find the first derivative of g(x) (x),6

A: As we know that: The product rule: f·g'=f'·g+f·g' The chain rule: fgx'=f'gx·g'x The Power law:…

Q: compute the derivative. y = sin(2x) cos2 x

A: We can find the derivative of this function by using the product rule of differentiation . According…

Q: 4) a) Determine the simplified expression for the 623rd derivative for the function f(x) =cos(2x)…

A: a)   fx=cos2x+sin2π     =cos2x+0      = cos2x

Q: 1. Find the derivative of the following sin² x cos² x a)y + 1+cotx 1+tan x

A: We have to find derivative of given trigonometric term.

Q: 17. Find the first derivative for J(x)=tan0x sec0

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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: 83. Find the 50th derivative of y = cos 2x.

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Q: 19. y = sin-1+ cos-1 2 2

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Q: 1-cos 4x Find the derivative of y sin 4x

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Q: 4. Find the derivative of the following function. 1+ sinx g(x) = - V1+ cos x

A: Given: gx=1+sinx1+cosx for finding derivative of given function, first we simplify given expression…

Q: Find the second derivative of f (x) = 9 sin (2æ). Enclose arguments of functions in parentheses. For…

A: Second derivative of f(x) is given below...

Q: 2. Find the derivative of y = tan°(/1 – x²). Make any obvious simplifications. %3D

A: Using chain rule of differentiation.

Q: Find the first derivative of the following function: 1. y = sin (2x) - cos (2x)

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Q: Find the derivative of the function. Simplify where possible. y   =arctan(cos θ)

A: Given:y=arc tancosθFormula:ddxtan-1u=11+u2.dudx

Q: Find the derivative of the function. Simplify where possible. y   = Cos-1(Sin-1t)

A: y=cos-1sin-1t

Q: (A) Find the first derivative of the following function: 1+ cos2x f(x) = %3D 1- cos2x |

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Q: 1.Find the derivative of the function y = cosh*x – sinh“ x - 2.Find the derivative of y = In cosh x.…

A: Q1)   Given  y= cosh4x -sinh4x         As per our guideline we supposed  to answer only first…

Q: Find the derivative of the function y = cot^-1 x2 – cos^-1 x + 1/x – 2 %3D

A: To find the derivative of: y=cot-1(2x)-cos-1x+1x-2...(1) Note that:…

Q: f(x) = sin (x³)

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Q: f(x) = arcsin ysin x

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Q: Find the derivatives of the functions defined as follows.

A: Given, y=-cos2x+cosπ6

Q: Find the first derivatives of y = cos x tanx

A: Given: y=4cos x+1tan x

Q: 2) Find the derivative of f (x) = tan(1 + cos 3 x) 3) Find the derivative of f(x) = Vx3 – 4x2

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Q: 3. Find if y³ + 2xy - x² = cos x using implicit differentiation.

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Q: 5. Find the derivative of --( 1 + sin 0 cos 0

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Q: 5. Find the derivative of h(x) = cos(sin(cosx)).

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Q: The function f(x) whose derivative is sin x and whose graph passes through the point(0, 2)​

A: we have to find the function f(x) whose derivative is sinx and whose graph passes through the point…

Q: Use the theorems on derivatives to find the derivative of the following function:   y = (cos(x))2 +…

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Q: Find the derivative of ?(?) = −7 cos(4?). using the chain rule

A: We have to find the derivative of given function using chain rule in differentiation.

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

A: To find The derivative of given f(x)

Q: find the equation of the tangent line to the graph of the function y = ln(x^2) at the point (3, 1).

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Q: 1. State the power rule. 2. For which values of n have we proved the power rule? 3. Based on your…

A: 1. The power rule of derivatives gives the following: For any real number n,      ddxxn=nxn-1

Q: How are the derivatives of sin-1 x and cos-1 x related?

A: Given functions are sin-1x and cos-1x