(b) Verify that f(x) = 2 cos(x) sin(1x). f(x) = sin(6x) + sin(7x) = 2 sin = 2 sin 6x + N 2 X COS 6x - | cos(- ž) 2

Q: cos( - x) = O sin( - x) O cos( + x) cos( - x) sin( + x)

A: The given expression is: cos π3-x Note that: cos θ=sin π2-θ

Q: Find the value →21. csc (sec- 2) + cos (tan¬1 (– V3))

A:

Q: For (cos(2x) – sin cos(x) – sin(x) - sin(2x) cos (2x)) +C. What is F (x)? A sin cos³ (x) – cos(x)…

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: f(x) = sin x In(5x)

A: Differentiate the function f(x) = sin x ln(5x)        Let f(x) = gh = sin x ln(5x)        where g…

Q: find the slope Of the followiny functions at the gruen point: at Xo to JL

A:

Q: Determine f'(x) for: Ax) = sin (5x - 2)

A:

Q: Q2/ Find f (x) : 1- f(x) = 4 cos x + 2 sin x 2- f(x) = cos x - x csc x 3- f(x) %3D %3D cot x 1+cscx…

A: As per guidelines we can solve only one question at a time. So the first question can be solved as…

Q: O t-sin(t)

A: the answer is t-sin(t)  provided the solution below with steps in step2

Q: What is the derivative of x 3 sin(x)? Select one: (sin(x) + 3x cos(x)) 2 Зх 3 + cos(x) 2 Зх 3 2 O…

A: Derivative of the function

Q: 3. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c)…

A: a) Use quotient rule of derivative and find the derivatives of above function.

Q: (a) y = In(sec²x) (b) y ecos + cos(e) x² −1+2 (c) y = x (d) y = sin² (e) y = (f) y = (cos(√sin(x)))…

A: Let's consider  the properties of differentiation.Let f(x) and g(x) are two different function…

Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

A:

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: Let ƒ(x) = (cos( − 4x – 5)) (sin(6x − 2)). Then ƒ'(x) =

A: f(x)=(cos(-4x-5))(sin(6x-2))

Q: cos(x1)=-1/3 sin(x2)=2/3 find 1. sin(x1+x2) 2. cos(x1+x2) 3.sin(x1-x2) 4.cos(x1-x2)

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: f(x) = 5 sin²(x) Hint: Use sin2(x) = -(1 – cos(2x))| %3D %3D n = 1 8.

A:

Q: Let f(x) 39 27 O 1 4√3 O-√6 9 3√3 .-1 (²). Then the second derivative at x = -1,f"(-1), equals = COS

A:

Q: Š 4 sin(3t) 2+ cos(3t) 7 sin(3t) + dt (2+ cos(3t))²

A: Definite integration

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

A:

Q: Determine f(x) a. f(x) = 4 sin² (x - 2) b. f(x) = 2(cos x)(sec² x)

A: (a) The given function is f(x)=4sin2x-2 Find the first derivative…

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: Calculate facos xdx . (a) rsinr – casz+c (b) Icosz+sin x+c (c) zcost-sin x+c (d) Isinz+cOSI+C (e)…

A: Formula for integral by parts :        ∫u(x).v(x) dx=ux∫vxdx - u'x∫∫vxdxdx+…

Q: d dx x= ||

A: Given that

Q: d dx [ 3+√√f(sin( sin(x)) cos(x) f' (sin(x)) 2√f(sin(x))

A: