d (i) Show that (2 dx -1 X 3x x tan 3 = tan-1* 3 x2+9 V3 i) Hence evaluate (tan dx . 3

Q: If f(x) = A B D tanx S™ 0 1+tan²x 1+etanx sec ³x l+etanx In (secx)√1+tan²x 1+etanx sec²x tanx 1+12…

A: Using the Leibnitz rule:

Q: Z and dy 없 of y%3 (5x2 - ) (cos ar d²y Determine (cos x + In x).

A:

Q: x sin wx O Show that dx = x² + 6x + 10 (3 sin 3w + cos 3w) w> 0

A:

Q: (a) [(0.6e15 + 4t 3t² +03-10-01 at 4t4-3t3 + 0.3 _10t 1.5 -0.1 2t3 (b) Evaluate…

A:

Q: d [ sin(x)cos(x) dx dx 1+x4

A: Find the integral

Q: |x In x dx 2. x3e3x dx 3. tan-1x dx / e* cos 3x dx 4. 5. fx*sin 3x dz Scos"1. Vx dx 7. sec-1. Vx dx

A: I have solved first three parts  For other parts please repost question It's bartleby guideline

Q: B. By miscellaneous substitution (VE+1)dx dx 1. S 2. S: 3 cos x+2 sin x-5 XA +

A:

Q: b) [F(x) then find f(x). If 3 In(x)/ sin(3x) − 3e³ + x² + 3. - f(x)dx= 3 ln([x]) + 3x + C

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Q: dy -is: then dx cos. cos x Q21. If y = tan 1+sin x

A:

Q: 3 tan-(x)dx O V3 - In (8) V3 TL In (4) 2/3 2.

A:

Q: Compute d/dx  sin-1 (x/x+1)

A:

Q: If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] True or False.

A: Given statement If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] is false.

Q: Find dy/dx if y= tan-1(x/(1-x))

A:

Q: e) у- In 2 2xe dx 1 dx xcos(In x) /2 g) y= V1+cos4xdx

A:

Q: // sin(7x²) dx dy. Compute O y/3

A:

Q: The approximation of I = = co cos (x²+5) dx using simple Simpson's rule is:

A:

Q: If y = sin(x + 4) cos(7 – x), then is dx A. sin(2r – 3) B. -sin(7–x) cos(x+4) C. cos(2r – 3) D.…

A: We have to find derivative

Q: The f sin x cos x dx is not equal to {A} -cos 2x + C {B} sin²x + C {C}-{cos²x + C {D} sin 2x + C

A: A detailed solution is given below

Q: tan x dy +y sin x dr = 0, when x = 0, y = | O y (3- cos 21) = 2 O y (cos 2x O y° (2 – cos 2x) = 1…

A:

Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…

A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: Evaluate: 1-11-24 = - dx 1 + x 0 By the trapezoidal rule with h = 0.5, 0.25 and 0.125 respectively.

A:

Q: 11. Integrate. a. x3 b. S(5 tan 3x – 2 sec2 x)dx

A:

Q: V sin2(x32 - 1) dx, with u x32 - 1

A: Consider the integral ∫(√x)sin2 (x3/2 - 1) dx.

Q: To evaluate 3cosx -1 1- sin?x dx, the integrand can be transformed to A J(3 cos x - sec²x) dx ® S(3…

A:

Q: 21. If y=(x* +sin x)", then dy dx (A) 6(x*+sinx) (4x-cos.x) (B) 6(x*+sinx) (4x' +cosx) (C)…

A:

Q: 2- Find dy/dx for y = In(tan(2x2))

A:

Q: The linear approximation at x 0 to f(x) = sin(6x) is:

A:

Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

Q: dy Find dx if y = cos (4x - 3x + 1) s*(4x²-3x + 1)

A: Given that, y=cos4(4x2-3x+1)

Q: S2ta J 2tan x In (cos x) dx=

A:

Q: 6 Evaluate (a) [ a + (4x-2° dx + (4x-2)* dx (2x-3)2 2x sin (x²+!) cos (x+1) dx

A: AS mentioned by you that "none of these is graded please answer 5. These are practice questions"…

Q: 1. Evaluate 1 (a) [ In(2x + 2)dx (b) [ sec'3x tan 3x dx

A: (1)(a) Use the method of substitution to solve the definite integral.…

Q: 5. y = l 1- co s x 1+co s x

A: We have to find out dy/dx for given y

Q: 2- y = prove that (sin x) = cos x %3D dx

A: Topic:- derivatives

Q: find dy/dx. y = x2 cos x - 2x sin x - 2 cos x

A:

Q: .2 1 2x -1 Prove that : sin .2 dx = 72 1+x 1+x?

A: Solution of given question is given step by step

Q: 6xsec 3x 2-If y = (tan3x)²² prove that = (tan3x)²= + 2ln(tan3x) %3D dx tan3x

A:

Q: Find dy/dx of y=sin -1(1/x). (A x²– 1 3 B 1- 9x2 1 9 D 1-x2

A:

Q: 25. æ sec (a²) tan(æ²) dæ | sin? x dx (Hint : cos (2x) 26. 1 27. dx 4- (ӕ — 1)? 1 dx 9x² + 25 28. dx…

A:

Q: find dy/dx. g(x) = cos x/sin2 x

A:

Q: Q1) find dy/dx 1) F(x) = sin’2x tan x² x – 3 ) 2) F(x) = sin( x +4

A:

Q: Find the derivative. d | dx + 0 OA. x³ sin (x¹) +5, ○ B. sint dt C. 4x³ sin (x4) - cos (x4) - 1 D.…

A:

Q: 1 a) 1+ sin(x) xp- Vtan (x)dx

A: a) Given integral is ∫11+sinxdx

Q: 1- find dy/dx as a function of x. y = sec (tan x)

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: Show that d 1 In cos(x) os(x) - csc(x) dx 1+ cos(x

A: We have to proof

Q: dy of y = sin(3x² + 5x – 4) * In(e*) is dx

A:

Q: Use graphs to evaluate 2π S 2r S 0 sin x dx = cos x dx = 2t S 0 2π sin x dx and cos x dx. 0

A: We will find the required.

Q: Find [(1 - cos² t)dt]. dx A. sin²x B. -sin²x C. 1 - sin²x D. - cos²x

A:

Q: Evaluate tan-1 x dx А. 1. tan-x dx = x tan-!x-;In(1+x²) + C В. 1. tan-x dx = x tan-x+;In(1+ x?) + C…

A: As we know that the expression for the integration by parts: ∫udv=u·v-∫v·du Given: I=∫tan-1xdx or…

Q: Find dy/dx if y = In (tan(x).3$ec(x) + /sin (x³)

A: given,