Expand the function f(x) = x, 0 < x < 2, in half range sine series. 4 O (A) (#) = - sin()- sin() - sin() - -- . ㅇ (B) f(쁘) %=D%= sin(플)-글sin() +sin()-. O (C) S(x) = sin(플) + sin() +sin()- .... 4. O (D) f(x) = sin(플) + 블 sin(2) -sin()

Q: For x = R, f(x) = log2 - sinx| and g(x)=f(f(x)), then (1) g'(0)=-cos(log2) (2) g is differentiable…

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Q: If h'(3) -1 and h'(1) = 5, then |h"(z)dr = %3D %3D (A) -6 (B) 4 (C) 5 (D) 6 (E) 9

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Q: y= 16 +. 16 tan' (7x) y=e

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Q: If f(x)= 8-cosh x/6+cosh x then f'(x)=

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Q: Find a formula for f-'(x) and (f -1)'(x) if f(x) = V х-2

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Q: Determine p′(x) if p(x)=ln(5x^2+x+6/x^3/5 tan(x)).

A: Given query is to find the derivative of the function.

Q: Find f''(x). 9 f(x) = (x² + 7) ⁹ f''(x) =

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Q: 3 Find a formula for f-'(x) if f(x) = ( x – 1 x + 1 f-'(x) = (5-1)'(2) =

A: Solve the function

Q: 7 Let f(x) = Find f'(x). (8x2 + 2x – 6)* f'(x) =

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Q: Differentiate. f(x) = 7+ 3e5x f(x) = 7+15e5x O f (x) = 7+ 5e3x f (x) = 0+15e5x

A: Differentiate the above function.

Q: Differentiate. f(x) = (3x – 4)(x + 4) ,1/2_Av-1/2 4x + 12 O A. f'(x) = 2.00x В. f (x) 3D4.5х 1/2 Oy…

A: NOTE: Refresh your page if you can't see any equations. .

Q: f f(x)=x3-x+2 find a formula for(without using d/dx) a. f'(x) b.f''(x) c.f'''(x)

A: Explanation: Given function: f(x)=x3-x+2 a) f'(x) f(x)=x3-x+2f'(x)=3x2-1+0f'(x)=3x2-1

Q: Find f''(x). f(x) = (x²+6) 6

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Q: let N= 1007276145 and f(x) = e^(x−1)(b − x). 1. Find f'(x), f^2(x), and f^3(x). 2. Find b such…

A: Given: fx=ex-1b-x Using product rule of differentiation (fg'x=f'xgx+fxg'x ) , we get…

Q: What are the intervals of monotonicity of f(x) = arctan (2(x-1)) - ln IxI ?

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Q: 8 x + 6 Let f(x) = x + 1 f'(x) =

A: The function is fx=x+6x+18. Find the derivative of the function using the chain rule and quotient…

Q: 4 Find f'(- 4) if f(x) = 6х. 3 f'(- 4) = || |(Simplify your answer. Type an integer or a fraction.)

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Q: L{f(at)}=(1/a)* f(s)

A: to prove the given problem . we use the definition of Laplace.

Q: 4. ƒ(x) = (x − 3)(x² + 6x-²) -√2: f'(x) 5

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Q: 7. Find the intervals of increasing/decreasing for the function f(x) = x'e*

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Q: If f(x) =x 3 -x find a formula for  f '(x)

A: Given fx=x3-x

Q: Sxg'(x) + g(x)f"(x}] dx = f(x)g(x) + C° %3D

A: To prove the following formula.∫fxg'x+gxf'x dx=fxgx+C

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.