0 ( -1 tan x du Q\ find dy if (xay sinx=(√√ au) - y² cosi'x

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: 3. y cos (sin'x)

A: For the given  y = Cos4(sin3x) dy/dx is calculated as shown below

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: dx sech x (3 +5 sinh x)

A: Please see the explanation below.

Q: 2. Find [cot (x)sin* (x)dx

A: First simplify then integrate

Q: Evaluate sin dx

A:

Q: Evaluate ∫ 3x2 sin(x3) dx.

A: To evaluate the integral  ∫3x2 sinx3 dx

Q: "/2 cost x dx "/4 sin6 x

A:

Q: -S * sin ´sin sin (e*) dx

A: we have to integrate

Q: Find f. f"(x)  =6 x + Sin x

A: Given: f"x=6x+sinx we know that f'x=∫f"xdx                                      ..1 so, by using…

Q: 1. sin° x cos x dx

A: sin3x cos4x  = sin(x) sin2(x) cos4(x)  = sin(x) (1 - cos2(x)) cos4(x)  = sin(x) (cos4(x) - cos6(x))…

Q: Find y' , for y=Sin-1(Cos√x)+Cos-1(Sin√x)

A: The solution for the above question is as shown below.

Q: s sec² x /1+tanx dx.

A: I=∫sec2⁡x1+tan⁡xdx

Q: 1. Simplify tan(x) sec(x) to a single trig function.

A:

Q: 7. f sinx cos³ xdx

A:

Q: 5. (a) 2e' sin? (b) e cos ?1

A:

Q: tanx sec² x.dx COS X √√2+ sin x dx

A: