₂2 Find the derivative of f(x) = ln ( ² sin x 2x+1 2 2 O f'(x) = + sinx - 241 x 2x+1 o f'(x) 2 X = = +cot x - 2 O f'(x) = ² + tan x + ○ f'(x) = 1/2 + cot x + 2 2x+1 2 2x+1 2 2x+1

Q: Find f. f ''(?) = sin(?) + cos(?),    f(0) = 4,    f '(0) = 2

A: f''(x)= sin(x) + cos(x) , f(0)=4 ,f'(0) = 2

Q: Find h'(x) if h (x) (2 csc x) (5 sin x - 3x). O-2 cot2 x (5 sin x - 3x) O2 cotx (5 cotx - csc x) -2…

A: Givenhx=2cscx5sinx-3x We know that cscx=1sinx We know that dcscxdx=-cscx.cotx Product rule for…

Q: f'(x) = Let f(x)= = I cos ³

A:

Q: Find the derivative of f(x) = In [sin(x) +x] Lsin(x)-x] %3D 2(sin x – x cos x) x2 - sin? x )2(x cosx…

A:

Q: Find f' (x) for 8 sin(x) f(x) = -; 7x2 – 8 sin(x) s'(x) = |

A:

Q: Find f'(x) if ƒ (x) = 6 cos x + 10 sin x. S'(x) =|

A:

Q: 2. Find the 2nd derivative of sin (x²-1) y *2cos(x^2-1) 4x^2 tan(x^2-1) 2cos(x^2-1) + 4x^2…

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Q: If f(x) f'(x) = = COs x 4 tan x, then f'(4) = Check Answer

A:

Q: (8) Find the derivative of the functions (i)h(x) = sin 2.x cos 2x (ii) f (x) = cos (tan 4.x) 1 =-…

A: We need to differentiate the given function. We will use different method of differentiation . ( As…

Q: Find f'(x) if f (x) = 2 cos x + 3 sin x. f'(x) =

A:

Q: Find the derivative of y = (cos x)* y' - -x sin x y! = COS X + In (cos x)| (cos x)* y' = x(cos x)x−¹…

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Q: Find the derivative of F(x) = 4 sin(t) dt. 3x %3D dx cos(x)

A: Solve the following

Q: Find the derivative a) y = x sinh-(x) – Vx² + 1 b) y = cosh-(2Vx +1)

A: The derivative is calculated as:

Q: Find f. f ''(?) = sin(?) + cos(?),    f(0) = 5,    f '(0) = 2 f(?) =

A: Given that        f"( θ) = sin(θ)+cos(θ)  The initial condition is f(0)=5 and f'(0)=2 We have to…

Q: F(x)=2x sin(x)Tan(x) find f'(x)

A: Use the concept of derivative of the form  f = uvw

Q: Find the derivative of y with respect to x. y = 5x4 sin-1 r 1 V1-x? + 20x3 5x4 1+x2 + 20x³ sin¬1 x…

A: We have to find the derivative.

Q: Find the derivative of each of the following functions, f(x)=sec(√x+cot(x)) a. F(x)= sec x sec (x +…

A:

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

A: Consider the given function

Q: The derivative of the function y = ecos²(x) is: y' = - sin(2x)eCos² (x) y' = sin(2x)eCos²(x) the…

A: We will find the derivatives of the given function y=ecos2x in the following step.

Q: 1) Find the derivative of f(x) = 1+sin 2x %3D 2 cos3 x

A:

Q: Find f'(x) if f (x) = 3 cos x + 8 sin x. f'(x) =

A: We need to differentiate the given Function.

Q: Use forward-difference formula to evaluate the first derivative of y = cos(x) at x = cos(x) at x =…

A: Given function is y=cosx. We have to evaluate the first derivative of y=cosx at x=π4 using a value…

Q: = 5 sec x tanx %3D

A: Please refer to the image below

Q: 2(1-x²) (1+x²)² A. f'(x) = B. f'(x) = c. f'(x) = D. f'(x): = f(x) = find the derivative of this…

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Q: Find f. f ''(?) = sin ? + cos ?,    f(0) = 1,    f '(0) = 3

A:

Q: Suppose h (x) =() . What is the correct result of the derivative of h with respect to x? ". In (5) A…

A: Derivative using chain rule of differentiation.