Differentiate the function f (x) = 4 cos 3x - 3 sin 4x. %3D O -4sin 3x -3cos 4x O -12(sin 3x + cos 4x) O 12(sin 3x - cos 4x) O 4sin 3x - 3cos 4x

Q: Find the first derivative of 2cos(2 + x³). a. -6x² sin(2 + x³) b. -x² (sin 2 + x³) c. -6x² (cos…

A: daf(x)dx=adf(x)dx ; where , 'a' is constant. dcos (ax)dx =-a.sin(ax) dxndx=n.xn-1 .

Q: Describe the method used to integrate sin" x cos" x, for m even and n odd.

A: The method to integrate sinm x cosn x when m is even and n is odd. We integrate by substituting the…

Q: Determine the absolute extreme values of the function f(x) = sinx - cosx + 6 on the interval 0 ≤ x ≤…

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Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: f(x) = ln(cos3(2x+1)5)     f'(x) = ?

A: Given that f(x) = ln(cos3(2x+1)5)

Q: Find the hundredth derivative of the function f (x) = cos(2x). O f(100) (x) = -2!00 cos(2x) O f(100)…

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Q: If f(x) = cos(x) +3z³, what is f'(æ)? O f'(x) = sin(x) +3z³ O f'(x) = sin(x)+ 9x² O f'(x) =…

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Q: Consider the function f(x) whose second derivative is f''(x) = 4x + 6 sin(x). If f(0) = 3 and f'(0)…

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Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

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Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 8 sin(x). If f(0) = 4 and f'(0)…

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Q: Find the derivative of cos(3x) O -3sin(3x) O 3sin(3x) O 3cos(3x) O -3cos(3x)

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

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Q: Find the ninety-ninth derivative of the function ƒ (x) = cos(2x). O f(99) (x) = 2 sin(2x) 99 f(99)…

A: Given : f(x) = cos (2x)    Times = 99

Q: Find the extreme values of the function f(x) = sin(2x) within the interval 0 < x < 2n %3D

A: Given function f(x)= sin(2x)            0≤x≤2π

Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: Match each function with its derivative. Y • x² x4 + 5x 1. cos x - - x8 8. sin x + x4 3x x4 -1.…

A: Concept: Differentiation of xm dydx=xm=mxm-1 dydx=ax=loge(a)· ax

Q: Find the most general antiderivative of the function. f(x) = 5 cosx-7 sinx

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Q: Find constants c1 and c2 such that F (x) = c1 sin 3x + c2x cos 3x is anantiderivative of f(x) = 2x…

A: Given: Fx=C1sin3x+C2cos3x and the antiderivative of F(x) is fx=2x sin3x To find the constants C1 and…

Q: Differentiate the function:  k(x) = 4 ln (x) + 2 cos x + x^2 k'(x) =

A: k(x)=4ln(x)+2cosx+x2Differentiate with respect to xk'(x)=(4×1x)+2-sinx+2xk'(x)=4x-2sinx+2x

Q: Solve for the derivative of the following trigonometric functions. 1. f(x) = e3x 2. f(x) = x³ ex 3.…

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Q: roo sin(2) Compute (4) dx. fo x(x²+4)

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Q: Find and locate the local and absolute extreme values of f(x) = x+(sin2x) in [0, π].

A: Find and locate the local and absolute extreme values of f(x) = x+(sin2x)in [0, π].

Q: Consider the function f(x) whose second derivative is f''(x) = 4x + 3 sin(x). If f(0) = 4 and f'(0)…

A: see the details solution in below

Q: 9. tan 4x sec24xdx d. cos 5xsin 5xdx e. x sin(3x² +1)dx f. [x* cos(2x' +1)dx

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Q: What is the derivative of y = 10sin 5x 5 In 10 cos x 10in 5x 5 In10 (10sin Sx) A. C. 5 cos x In 10…

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Q: Let f (x) = sin(4.x). Find the twenty-second derivative of f (x). D22 (f (x)) = O 42² cos(4æ) - 422…

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Q: f(x) = cos (In (3x))

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Q: Use the method of undetermined co – efficient to solve: y'' + 2y = sin (x)

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Q: Find the hundredth derivative of the function f (x) = cos(2x) . O f(100) (x) = -2100 cos(2x) O…

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Q: Find if dy dx y = (cos x) * O (cos x) * (-sin x) O (sin x) * (In cos x - x tan x) O (sin x)* (In cos…

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Q: Q3- Find: 1- Sv2 + sin3x . cos3x dx. 2-5* dx x5-2x sin 2x 2 sin x 4- f cscx cot x dx 4 cos x 5- S 3+…

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Q: Linearize f(x) = 5 cos x about x = pi over 2. f(x) = -5x

A: linearization around x=a is given by :L(x)=f(a)+f'(a)(x-a)

Q: The derivative of f(x) = ln( is cos x - Select one: O f'(x) = sinx O None of the other options O…

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Q: find the most general antiderivative of f(x)= 2x^3 - sinx + 4e^x

A: We find the integral of f(x)= 2x^3 - sinx + 4e^x We separate the integral first.

Q: Find fif f'(0) = 2 sin 0-sec²0

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Q: Find the derivative of f(x) = 2x(sinx)cos(x) ? a. f(x)=sin2x+2xcos2x b. f(x)=2sin2x+2xcos2x c.…

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Q: Evaluate sin (4x) cos -2(4x) dx. | sin (4x) cos -2(4x) dx = O

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Q: Find the linearization of ƒ(x) = sqrt(1 + x) + sin x - 0.5 at x = 0

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Q: Evaluate /(e* + - + cos4x)dx O + logx + sn3x +c e2r 3 4 e3x sin4x + logx + + c 3 2 O + logx + e5x 2…

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Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts, ∫cosn x dx=cosn-1 x sin…

Q: (b) Verify that f(x) = 2 cos(x) sin(x). f(x) = sin(7x) + sin(8x) 7x + 7x = 2 sin 2 = 2 sin |co(-)

A: Let the function is  f(x)=sin(7x)+sin(8x)   Formula used: Sin(a)+sin(b)=2sina+b2cosa-b2

Q: Evaluate the integral cos3 x + sin² x + 1 dx cos² x (sin2 x + 1)

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Q: What is q'(x) when q(x)=ln((5x^2+x+7)/((x^2/3)(sin(x)))

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Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: Differentiate implicitly for the equation for x^2y+x^3-cos(x)=3y^2

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Q: Given the function y = 6 cos(3x + 1) The second derivative y" %3D Select one: 18 sin (3x + 1) -18…

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Q: Differentiate with respect to the independent variable. f(x)= (e^x + cos x)^6 (3x^4 - sin x)^2

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Q: Find the ninety-ninth derivative of the function f (x) = cos(2x) . O f(09) (x) = 2% sin(2x) f(99)…

A: Let's find.

Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 10 sin(x). If f(0) = 3 and f'(0)…

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Q: . The derivative of y = 3VX4 – cosx is - D. x*/3 + cosx A. x/3 + sinx В. 4х /з + sinx C. 4x*/3 +…

A: y=3x43-cosx⇒y=3x43-cosxThen dydx=(3×43×x43-1)-(-sinx)                           =4x13+sinx