Q1:Find dx for the following a) y = tan-(sinx) + In (sec2x) + 8tan5x + etm

Q: Differentiate y = sin (x 2)

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Q: (f) / sec“ y dy. tan5

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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: Differentiate y = (-6+sinx)/(x+cosx)

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Q: Determine 3 sec(9x) tan (9x) dx

A: We have to determine the value of integral: ∫3 sec 9x tan 9x dx Solving given indefinite integral by…

Q: Find sin (2)dr (hint: use a half-angle formula twice).

A: Note: sin2x=2sinxcosx  Cos2x=1-2sin^2(x) And sin^2(x)+cos^2(x)=1 by using these formulas we solve…

Q: 8 him XT 2 (secx tanx) 1

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Q: (tan V) (sec V) b) Evaluate dx

A: Given integral: I=∫tan4(x)sec2(x)xdx

Q: Differentiate y=sinx+cosx+tanx

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Q: Stan³ x secx dx

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Q: Q4 Evaluate: f(1- cos²4x) sin4x dx.

A: The given integral is: I=∫1-cos24xsin4xdx   As we know the Power rule. ∫xndx=xn+1n+1+C

Q: (tan"Vx ) (sec²/x) dx Evaluate

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Q: Evaluate tan (8x) sec*(8x) dx.

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Q: y = Secx ( sinx+ Cosx)

A: Given, y=secxsinx+cosx And we have to find the dydx.

Q: 6) Differentiate: a) y = 2x - x² tanx

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Q: @) find 16+9X 2

A: Question (1) - Let the given integral be y - y = ∫043 316+9x2dx          Taking 9 common from…