If f'(x) = cosx - 9x² + 1 which of the following could NOT be f(x)? 1 A f(x) = sinx - 3x3 + Inx + B f(x) = sinx - 3x3 + Inx - 2 © f(x) = sinx - 3x3 + Inx 1 D f(x) = sinx - 3x3 + Inx + /2

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh x cosh(2x) = cosh2 x + sinh2 x

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Q: Find the Derivative f(x) = cosh(In(4x))

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Q: 3x+4 3. f(x) = x2+3

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Q: Integrate sin^2(7x)-cos(x)

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Q: if f(x)=ln(1+cosx) then find f`(x)

A: f'(x)=(1+cos(x))'/(1+cos(x))      =-sin(x)/(1+cos(x))

Q: find f'(x) if f(x) = tanh(ln x) +sin2(2x)

A:

Q: How do I verify d/dx(cos^-1(x))=-1/(sqrt(1-x^2)) using implicite differentiation?

A: Verify the result by implicit differentiation as follows.

Q: 1) Find 4 by implicit differentiation given 4 cos x sin y = 1. dx

A: Differentiate above equation with respect to x.

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: Find the function who’s derivative is dy/dx = tan(x)sec(x) - 9x^2

A: Given: dydx=tanxsecx-9x2   As we know that; The Power Rule: ∫xndx=xn+1n+1+C And the common integral.…

Q: If f(x) = x cosh æ + 3 sinh x then f'(x) =

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Q: 1. f(x)= Vx3 + 2x² + 3 2. f(x) = (6x – 7)(2x + 3)

A: To find the second derivatives of the given functions.

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: The first derivative of y=cos(tan(x2-7x+1)) is.. 1. O -[sin(tan(x²-7x+1))][sec²(2x-7)] 2. O…

A: Find the derivative of y=costanx2-7x+1

Q: If f(x) = x cosh x + 5 sinh x then f'(x) =

A: Find the derivative

Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: sinh(9x) If g(x) : 8 + cosh(9x) find g' (x) 8+ cosh(0)

A: Following formulae are used to solve first question

Q: Verify the formulas by differentiation. ∫ sec2 (5x - 1) dx = 1/5 tan (5x - 1) + C

A: ∫sec25x-1 dx=15tan5x-1+C

Q: 7. The derivatives of the function f (x) = cos(3x²) that follow are incorrect. What misconception…

A: The differentiation of product two functions can be calculated by using the formula,…

Q: f6)= Sin () (x 3x26x-8) 1 CosX In Ceos x) | $66)=Sinx+t Cosx. sinsetl -6()=DSin -2053 2.

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Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: f(t) = In Itsinx 1-sin x g(x) = x sin ¹3x + √1-9x² G(x) = x In (9 + x²) + 6 tan-¹ (-)-2x

A: Note: Since, in the first function there is a typing error "f(t)", it should be "f(x)" because it is…

Q: Choose the derivative of sin (x). - 1 1 1+ x2 1 x2 | 1 1+ x2 1 xVx2 1 - 1 V1- x?

A: It can easily find the derivative of function

Q: : Find value of x if :- 2 sinh (2x) - 4 cosh (2x) = - 4

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Q: Find the derivative. 5х + 1 In 5x - 1 dx 5x +1 %3D dx 5x -1)

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Q: find the root of 3x +sinx -e ^x=0 using secant method

A: Let us consider the function fx=3x+sinx-ex. We have to use the secant method to find the…

Q: Compute sin x dx er + 3e -x 8.

A: We have to compute the given expression ∫sinxex+3e-xdx from -∞ to ∞ Therefore, The  given expression…

Q: Verify the identity. sinh2 x = (−1 + cosh 2x) /2

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Q: Find the derivative of x2cosx+2xsin x O 2xcos x O x² sin x + 2xcos x Ọ xzcosx y=x²sinx

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Q: Find a function with the given derivative whose graph passes through point P f'(x)= 2xx+1-cosx,…

A: To determine the antiderivative satisfying the given initial condition

Q: Find the derivative of the function. h(x) CoS x 6. %3D 1+ sin x sin x -61 coSX --6 cosx (1+ sin x)6…

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Q: sinx In (2) co cos x

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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: Find* esin ¤ dx tan x csc x cos x e $in xt. - cos x e Sin x + c Option 4 Option 2 esinx + c ,sin.…

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Q: find the first derivative of the function. F(x)= (1+sin2x/1-sin2x)^3

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Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) 1 1 -In(бx? + бх — 4) + arctan x- -(12x + 6)…

A: Product rule (u v )' = u ' v + u v' Formula derivative of xn=n xn-1 Derivative of arctan…

Q: Find the first derivative of  y = cos4 x – sin4 x y = x3   –  x2 cos x  +  2x sin x  + 2 cos x y…

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Q: 4. Use implicit differentiation to find az in xexyz sin(2z) – xyz = 5. ду

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: limit x to 0 3x-3xcox/sin^2(3x)

A: Here given limit as Use the L'hospital rule which states

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

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Q: If f(x) = sinx + cosx sinx - cosx 2 show that f'(x) = sin 2x – 1

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Q: Find the derivative of: sin sin(2x) sin sin(x) + cos (2x) cos(x) ans: -sinx solution?

A: We will use the formula cosA*cosB+sinA*sinB= cos(A-B) , with A=2x and B=x and simplify.

Q: Find the derivative of f(x) = ecos² (3x+1) Of(z) 6 sin(3r+1) cos(3x + 1)ecos² (3+1) O (E) None of…

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Q: Find the derivative. Simplify completely. 1. f(x) = 4x³ cos x 2. g(x): Sx-4 In x 3. у sin x 4. f(x)…

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Q: second order derivative of (5 sin 3x+cos^2 (3x )) is *

A: The function: y=5 sin3x+cos23x

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: If g(x) : 8 + cosh(9x) find g'(x) 8+ cosh(0)

A: Answer and explanation is given below

Q: Evaluate ax xm-1 sin bx dx in terms of Gamma function. -ax

A: We use the special results of Gamma function to solve this problem as in next step.

Q: Solve for the derivative of the Trigonometric Differentiation. 1. y = sin (5x) + 3x cos (5x) 2. y…

A: given y=sin5x+3cos5xdiffrentiate w.r.t. xdydx=ddxsin5x+3cos5xdydx=ddx(sin5x)+ddx(3cos5x)we know that…

Q: 3-sinx 6. f(x) = 1+ In(x3 — х)

A: Quotient rule of differentiation: Chain rule:   also