Evaluate tan" (x) sec²x dx m 1 1 n (m + 2)(x) + tan -tan" (x) + C m+2 m 1 -tan (m + 1)(x) — . m+1 m-1 1 -tan (m + 1)(x) + m+1 1 a (m + 3)(x) + m+3 - -tan -tan (m-1)(x) + C -tan (m-1)(x) + C -tan (m + 1)(x) + C 1 m+1

Q: [CLO-2] Find the derivative of 5 cosx f (x) = 4 sinx+3 O 21 – 6 cosx O ( 7 cosx+2)2 6 – 10 cosx (3…

A: Given:         fx=5cosx4sinx+3   Differentiating on both sides       f'x=ddx5cosx4sinx+3 Taking…

Q: Let f'(x)= = f(x) = x² tan ¹(7x)

A:

Q: If f(x) = tan (3x), then f'(x) = (A) 12 tan (3x) sec?(3x) (B) 4 tan (3æ) sec2(3x) (C) 12 tan (3x)…

A: derivative

Q: Differentiate g(x) = (In(x² + 1) – tan-ª(6x))10

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Q: y = 2sec? (4x) + tan*(4x) %3D

A: We will find the first derivative.

Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

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Q: Find the derivative of y with respect to x. y = sin* 17 2x 2 √√49- (2x + 1)2 2 1 + (2x + 1)² 2…

A: Given:y=sin−1(72x+1​)Solving for the derivative of y with respect to xdxdy​=dxd​[sin−1(72x+1​)] The…

Q: 1-S 1-sinx dx 1-sin?x -sin²x

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

Q: Find the derivative of y sin ¹(3x) x sin ¹(3x)-3x√1-9x²-9x² sin ¹(3x) x² (1-9x²) sin…

A:

Q: 3x2-7x+8 f(x) = Find f'(x) %3D sin (5x2+9x-6)

A: Here we use division rule of differenciation.

Q: Evaluate / 3 x sin(x)dx 03 (sin(x) – x cos(x)) + c Osin(x) – x cos(x) + c 03 x sin(x) + 3 cos(x) + c…

A:

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: Evaluate V(4r + 12)– 6 lim Зх- 18

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

Q: * Evaluate. (sec6(x)) dx

A:

Q: integrate (sin(x)*tan(x)-cos(x))/tan (x+1)

A:

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

A:

Q: What is the derivative of −9 sin² (-3x³)? O-162x³ sin (-3x³) cos (-3x³) no correct answer O 162x²…

A: just differentiate the given function by using chain rule of derivative and easily find the required…

Q: ● ftan(x) sec(x) dx

A: We will use substitute method to solve the integration

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

A:

Q: f(x) = 4sin (1-3x2) + xcosx-9, then f'(x) = -24xcos (1-3x2)+cosx-xsinx True O False

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Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Let h(x) = tan(2x + 8). Then h'(3) is and h''(3) is

A: This question is about application of derivative

Q: Ssin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) sin(2x) SinZx [cos(2x) – 1]+ 8 * + C + 12 sin(3x)cos(3x),…

A:

Q: dx J x²–18x+97 O fIn (x² – 18x + 97) + C In (x² – 18x + 97) + C 0sin-l (부) + C х-9 O tan-' () + C…

A:

Q: Let f(x) ƒ'(x) = ƒ'(3) = = √2x² + 4x + 3

A:

Q: Find sec2 (2x) 1- S (tan2x-4)9

A: Since multiple questions are asked, according to guidelines I am solving the first question. Please…

Q: (a) [In(4) - 2e¹³] dx d b) dx d (c) [2²² - 1 (2²)] = 4e³x In(x [sec (12r) + tan-¹(2x)]

A: NOTE: Refresh your page if you can't see any equations. .

Q: (d) v1+ tan x =1+;x

A: To prove that the following approximation holds, 1+tanx≅1+12x