Consider the following steps in 2 differentiating f(x) = ln x² sin 2x Identify the line number where the FIRST ERROR occurred. f'(x) = 2ln .D. [In (sin ²2r)] sin 2r (1) f'(x) = 2ln -D₂ (2)] sin 2x (2) sin 2r 2² 27). [(sin 2x).. · [(sin2x).((^ f'(x) = 2ln 2)D, (sin 2r))] sin 2x (3) f'(x) = 2ln (Sim2). [(Sin 2²r) (sin 2r) D. (2²) — (1³)D, (sin 2r)` sin² 2.x (²) (cos 2x)\ sin² 22 (sin 2x) (2x) sin 2)(cus 2x))] O Line (1) 3

Q: 3x+sinx-3 tan x -) Given g(x) = ln- calculate g'(x). %3D 3x4-Vx

A: Given gx=lnx3+sinx-3tanx3x4-x We know that lnab=lna-lnb. Therefore, using this formula we can write…

Q: dp Find dx given p(x) = (sin?(3x))(3x²-4*)

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

Q: QI) Show that: (a) (1+x)° =1+6x (b) (cosx) = –sinx dx

A: 1.  a  1+x6≅1+6xb  ddxcos x=-sin x

Q: If find f'(x). Answer: f(x) = 4 sin x 3 + cos x

A:

Q: Find sin (x) if sec (x) sin (x) A = B = B = 26 24' where tan > 0. Put your answer in reduced form.

A:

Q: 2 sin x f(x) = 2+ cos x find f' (x).

A: use ratio rule for finding the derivative of rational function.

Q: Find the first derivative of y = Arc tan √x² −1+ Arc csc x 2 O 2 O 0 2 Ox√²+1

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

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: If f (x) = -4 sin x – 6 In x, find f'(x). f'(x) =

A: The given function is f(x)=-4sinx-6ln x

Q: C- Find f' of the following: 1) √2x³-2² + In ² 2) 3xe³r+1 3) sin ¹(³).

A:

Q: If f(x) = sin?x, then f"(x) = %3D A 2cos2x B cos2x -sin2x D -4sin2x

A: Given, f(x) = sin2x For the given function , applying chain rule ,  First differentiate it as { xn ,…

Q: Let f(x) = 3 cos(x) sin¬(x). Find f' (x). f'(x) =

A:

Q: Plot the following function 0 <x< T sin(x) f(x) = } -0.81x2 + 7.64x – 16 π<x< 2π -1.62x2 + 25.46x –…

A:

Q: Given: f(x) = 1– sin² 4x . find the 5th derivative

A: