far 4 (4f² + 3)² dt cos t dt 1 + sin t sec x tan x dx sec x – 1

Q: y'tan x sin 2y = sin² x + cos² y.

A: We need to solve y' tanx sin2y=sin2x+cos2y This can be written as: y' tanx…

Q: 2 [(3 sec2 x + - x)dx 4

A: Integrate

Q: Evaluate the following integrals -3.r/4 + 8a*]dx -3

A: Since there are multiple questions present, according to company policy we will be answering only…

Q: Q3) find the derivative of each function: 1) y=x sin 2x +x cosx

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

Q: y = x * (sin 1x)² – 2x + 2v1-x² * (sin-1x), Find dy dx

A: Given that equation of y and we find dy/dx. We know that d(sin-1x)/dx = 1/√1-x2. And d(xn)/dx =…

Q: dy for the following functions : dx 1. Find 3(x – 1) (ans.: 5) Sec² /2x +7 15) y=\tan /2x +7 (ans.:…

A:

Q: Evaluate dy/dx at the point (π/2, π/2), if 2 sin^2 x + 1/2 cos y = (3 sin x)^11 . Mention all…

A:

Q: 1+sin 2 x 1) Find the derivative of f(x) %3D 2 cos3 x

A: The given function is                                    y=f(x)=1+sin2x2cos3x…

Q: Find f'exo if fex)= Find f'ex) if fcx)= (5x² + 1) cos(2x) 100 sec² (2x + 5) (x + 2)¹ 3

A: fx=5x2+1cos2x3sec22x+5x+2100

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

A:

Q: find dy/dx 4x -x 2x 23) y= Sin- +x².Sec 2-x + 2x.Sec) 2 (ans.: (2-2»N(2-x² - x* 4 4

A: To find the dy/dx means y' of the given function

Q: Solve the equation (y - (cos x)^2)dx + (cos x) dy = 0

A:

Q: Determine f(x) a. f(x) = 4 sin² (x - 2) b. f(x) = 2(cos x)(sec² x)

A: (a) The given function is f(x)=4sin2x-2 Find the first derivative…

Q: 1 [In(3x)] S (* -5x+2)e*dx

A: solution is given below

Q: dt dp dt о dp dt о dp dt S 3t tan 3t = 3sec t tan 3t 3sec3t tan 3t = 3 sec 3t

A:

Q: Q1) Use implicit differentiation to find dy/dx if a) (3xy + 6)2 = 7y b) x cos(3x + 2y) = y sin x %3D

A:

Q: 1½-sin² x 2 x. Find the second derivative of y = ½ sin Oy" = COS x Oy" y" = cos² x - sin² x о 2 y" =…

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Q: Solve to Find if cscx – San () dt = 4 – y?

A:

Q: 6) y = (sin¬1 8t) (sec -1 derive

A: First, we use the product rule

Q: Find dx (e3t + 1)dt. -cos(3rx)

A:

Q: H.w Sec'c-x)=バーSec x

A:

Q: The derivative of y =e' ,In(sin 2x) is a) y = eln(sin 2x) sin 2.x b) y = e a(sin 2x), cos 2.r c) y'…

A: