V dx d dx d dx d dx d dx -sec-¹(x) tan-¹(x) cos-¹(x) csc-¹(x) d dx sin ¹(x) cot-¹(x) 1. 2. 3. 4. 5. 6. 8. assa 9. H M 7. H TARA - BEOGEN - - arcsin (r) darctan (x) arcsec (x) dx d dx 1+x² 1 |x|√x²-1 COS X 1 sec²x 1 sec(x) tan(x)

Q: 1. Dx[arcsin(2x + 1)]

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Q: 2tanx/1-tanx = 2/cotx-tanx

A: Consider the given trigonometric expression 2 tanx1-tan2x=2cot x-tan x

Q: arcsin(4x)/arctan(5x)...

A: Using L'Hospital's rule to evaluate this limit,we know that,if  is of the intermediate form or…

Q: 3 sin° x -dx Evaluate ' cos° x

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Q: Find dy/dx of inverse tan(1/x) multiplied by secant(x)

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Q: 2. Explain why arcsin(sin(0)) = 0 but arcsin(sin(807)) # 807

A: Concept  arcsin(sin x) = x   is true  only when x lie in the interval [-π/2 , π/2]

Q: Find d/dx (arcsin (π/x^2))

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Q: 8.) k(x)=-2 tan(2(x+)) Period = Increment =

A: Given function is: kx=-2tan2x+π8 Then the period of this function is 2π2=π. The increment is π8.

Q: tan°(x) sec²(x) dx = 1/7tan^7(x)+1/9tan^9(x) %3D

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Q: V3 Tan" (-V3) Cos"(-1) 3. Sin 2 1. 2.

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Q: arctan(2x) arcsin(see (7), find f

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Q: Let 5 sin⁡x+ 7 cos⁡ y=6. dy/dx= d^2y/dx^2

A: 5sinx+7cosy=6Differentiate w.r.t x5cosx-7sinydydx=05cosx=7sinydydxdydx=5cosx7siny

Q: arcsin(4x) arccos (x)

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Q: x? sin° (x³) cos³ (x³) dx cot3 -x ) csc³ dx X- 2 | (3 – 2 tan? 5x) sec2 5x dx

A: We will solve the following