sin^2(x/2)=(tanx - sinx)/(2tanx)

Q: Find the derivatives of the functions in Exercis

A: Differentiation of the rational function can be done with the help of the differentiation formula…

Q: If f(x) =sin x sin2x sin3x find f" (x)

A: Given f(x) and find second derivative of this function. We use trigonometry relations and derivative…

Q: 3 sin° x -dx Evaluate ' cos° x

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Q: ∫ 2cos^2(x)sin(3x)dx

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Q: solve for x so that sin[2(tan^-1(3/x))]= - 3/4

A: We have given sin2tan-13x=-34 Then,…

Q: Differentiate f(x) = tan(6x). Use exact values. f'(x) = %3D

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Q: First Derivative:  w=sec2x+tan2v

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Q: temperature values ​​are measured every hour in a day and a mathematical model is created for the…

A: The formula to find average temperature is  Ta=1b-a∫abT(t)ddt Here b=12 and a=0

Q: y = 2 7x²)*(1 + 9x)² (sec²(x^))(tan³(x¹)) (x³ - 7x²3) 4 (1

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Q: solve (sinx)sec^2(x)+(cos x)cosec^2 (x)=0

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Q: verify cos(3x) = 4cos^3 (x) - 3cos(x)

A: We know that  cos(A+B)=cosAcosB-sinAsinB Therefore cos(3x)=cos(2x+x)=cos(2x)cos(x)-sin(2x)sin(x)

Q: please find the derivative of (x5 - 2)/sin (3x) + 5

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Q: Find f'(x) where f(x) sin(cos(4x2 +1))

A: Consider the given function

Q: Sin (플-) sec(-x) =

A: To solve sin[(π/2)-x] sec(-x)

Q: Determine f'(π/4) if f(x) = (tanx)/(1+cosx)

A: Solve the given differential using the basic formula of differentiation.

Q: cscxdx 5+ cos²x sin²x

A: Evaluate: I=∫csc2x5+cos2xsin2xdx We know that, cos xsin x=cot x Then, we have I=∫csc2x5+cot2xdx

Q: limx→0 (sin6x)/(tan6x)

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Q: ∫√1 - sin^2 x dx

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