Prove that: (ja) 2₁ ( 1 , ² ; 3 ; x ²) = ↓ sin^¹ x (b) 2 E1 3 2 1 tan 1 x

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A: In the given question, the Fundamental Theorem of Calculus Part I is applied. ∫afxgtdt=gfx·f'x

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A: f(x)=sin2(3-x)

Q: 7) Find f(e) if a) f'(;) = { x and f6)=2 D f'(x)=\+sinx & f 3.

A: Here we find the f(x) using integration.

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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: Differentiate each function a) f(x) =sin'[ (tan (cos (x²)) ] b) g(x) =/ sec(x* +2x) c) h(x)=V5 +3x²…

A: As per our guidelines we need to solve only 3 subparts.please repost the remaining subparts as other…

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Q: Let a € R, and define vectors u₁, U2, U3 € R³ in terms of a by E] 2 U₂ = a U₁ = 3a +3 2a +3 a² + 3a]…

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Q: Find f if f"(t) = 2et + 3 sin(t), ƒ(0) = 2, ƒ(π) = 5. f(t) = = 2e^t-3sint+ (2e^(pi) - 5)/(pi)t

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A: Given equation is: xy2+x tan y=y sin x We have to find dydx.

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A: Given query is to find indicated derivative.

Q: Let f(x) = tan ¹(sin(8x)) f'(x) = > Next Question

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Q: x' sin (tanx*) -1 Integrate 1+x

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Q: Given f''(x) = – 9 sin(3x) and f'(0) = – 4 and f(0) = 5. Find f( %3D

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Q: +(x)=sin' (tan 3x) 1-

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A: As per the company guildlines we can solve one question. Please understand.

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Q: If f(x) = 2 tan '(5 sin(3r)), f'(x)-

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