1) Find the derivative of f(x) 1+sin 2 x %3D 2 cos x

Q: f(x) = acos(b\x) x2 COS

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Q: 4. Find the derivative of the function f(x) = (sin x)c0s ". COS x

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

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

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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: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: 2) Find the derivative of f(x) = tan(1+ cos 3 x) %3D

A: As the function involved function in a function we can apply chain rule and find the derivative of…

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

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Q: 2. Find the derivatives of Y with respect to x if; x=arc sin ex.

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Q: Find the derivative of y with respect to x. y = 2x 4 sin -1 x

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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 g(x) = e * x). sin (1+ 0-3x²e*cos(1+x°) O xe*1sin(1+x°)+3x²e*cos(1+x) O…

A: The product rule of derivatives states that duv=u'v+v'u.

Q: 1 Find the derivative of g(x)= (x)sec(x) + a+ x* + cos - sin(x)

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Q: 13. Find the derivative at x = a for f(x)= /sin(4x) 2 Vsin(4a) cos (4a) Jsin(4a) 2 sin(4a) Vsin(4a)…

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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: Find the derivative of the function. f(x) = sin-(4x) f'(x) = %3D

A: The given function is: f(x)=sin-1(4x) To find f'(x) here.

Q: Find the second derivative of f (x) = 2 sin (3x). Enclose arguments of functions in parentheses. For…

A: Differentiate two times

Q: 12. The derivative of cos(1 – x) with respect to x is ;A. - sin(1 – x) B sin(1 – x) C -(1– x) sin(1–…

A: Given that: Let f(x)=cos(1-x)

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: Find the derivative of y with respect to x. y = 5x4 sin-1 r 1 V1-x? + 20x3 5x4 1+x2 + 20x³ sin¬1 x…

A: We have to find the derivative.

Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: Find the derivative of the function. f(x) %3D еx sec(9x) cos (9x) · e* + 7e* · sin(9x) f'(x) C cos…

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Q: Find the derivatives of the functions y = x2 sin4 x + x cos-2 x

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Q: Find the derivative of the function tanh-e* A. -1/2 csch x B. 1/2 csch x C. -1/2 csch 2x D. -1/2…

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Q: (a) Find the derivative of the function g(x) = sin2 x + cos2 x (b) then use a trigonometric…

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Q: Find the second derivative of f (z) = 6 sin (5z). %3D Enclose arguments of functions in parentheses.…

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Q: Find the derivative of sin 0 f(e) = 1+cose 1 + cos O 2)

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Q: Assuming that the derivative of arcsin(x) is indeed 1/√1 − x2, supply the justification that allows…

A: Recall the power series expansion for 1/√(1 − x2) The same  can be written as: 1/√(1 − x2) = c0 +…

Q: 2. Find the derivative of the function. y = e* In (sinæ)

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Q: Find the derivative of the function: f(x) = [sin(4x + x)] [cos(x4 + 4)] f(x) = e3x²+*(cscx + secx)2…

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Q: Sin X I+ COS f' (x) =>

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

A: Using chain rule of differentiation.

Q: find the derivative of sin (ax + b) cos (cx + d) CX

A: According to product rule of differentiation ,and according to chain rule of differentiation ,.

Q: 3. Find the derivative of f(x). (a) f(x) = e cos x (b) f(x) = (2x³ 4x-¹) cotx -

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

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Q: 17) Find the derivative of y = x? COs x - 2

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Q: 1) Find the 3rd derivative of y = sin(x) %3D

A: To find the 3rd derivative of y=sinxx. Solution: For finding third derivative, we need to find first…

Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used:…

Q: 2 a) FIND BY IMPLICIT DIFFERENTIATION: x*y³ = -8 %3D dx b) EVALUATE THE DERIVATIVE FROM PART a AT…

A: Given: x4y3=-8

Q: Compute the derivative for y= (e^-4x sin^2(x)) / (x^2 + 3x + 1)

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Q: Find the derivative of f(x) = 3r sin(-)(x) – In(r² – 1) + 8² – 5 cosh(x)

A: Find the derivative of function

Q: b. Find the derivative of y = Scos (x) sin(3–2x) + tan2(3x² – 4x) – csc(V2x – 1 Jand express your…

A: To find the derivative of below equation

Q: 1. Find the second derivative of y = sec-'x+ csc-!x. a. 0 b. C. +x+ d. -1 2. е.

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

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

Q: |sin x.cos x %3D 1+ 2.ln x

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Q: Solve for the derivative of the Trigonometric Differentiation. 1. y = sin (5x) + 3x cos (5x) 2. y…

A: given y=sin5x+3cos5xdiffrentiate w.r.t. xdydx=ddxsin5x+3cos5xdydx=ddx(sin5x)+ddx(3cos5x)we know that…

Q: 3. Find the derivative of (a) f(x) = (x+ 4 sin æ) (1 – 6 cos a), an (b) sin r g(x) %3D 6x

A: a). Given function is fx=x+4sinx1-6cosx. To find the derivative of given function. Solution: Product…

Q: 1) Find the derivative of the function: (3х — 1)3 Vx* — 1 f(x) = cos² x

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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

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