fip Ify r' sin I, dx a)3x²+ cos x 3. O b) 3x sin x + x° cOS I O cos x 3x sin x + x³ COS 2 Od 13 sin(1) Oel 3x2 sin x x' cos x 近。 N

Q: 2. Prove the following identity: sin (x+y)sin (x-y)=cos² y-cos²x X =COS - COS¯ x X.

A:

Q: tan x-7 3. Differentiate. y = secx Select the correct answer. dy bl dx a) = 7 cos x + sin x = cos x…

A: Note that derivative of sinx is cosx and derivative of cosx is -sinx

Q: DI Ify x Sin x, x'sin x, .2 O a) 2 sin +x cos x O b) 2x sin x + x I SOƆ cos x O) 2x sinx - x cos x…

A: Use product rule of differentiation. D(uv) = D(u).v + u.D(v)

Q: sin x a) 1+cos2 x dx

A:

Q: Let x² + sin(yz) = xz² + y dz and ду dz Find

A: Given,           x2+sinyz=xz2+y

Q: Step by step

A: We will need integration by parts for this problem. So we assume u and dv then find du and v

Q: Find y" if y = 5x sin x. O A. y" =5 cos x- 10x sin x O B. y"= - 5x sin x OC. y"= - 10 cos x+ 5x sin…

A: Solution: The objective is to find the double derivative of the given function

Q: Let 6 sin x + 3 cos y = 4. dy dx d²y dx² -0

A:

Q: Prove siny-2 sin³ y 2 cos³ y-cosy = tany ✔✔✔

A: The given identity .The aim is to prove this identity.