If f is a differentiable function, find an expression for the derivative of each of the following functions. (a) y = x²f(x) Ⓒy' = x6f '(x) - 6x7f(x) O y'=x7f'(x) + 7x6f(x) Oy' = x7f(x) + 7x6f '(x) O y'= x7f(x) - 7x6f '(x) O y'= x6f '(x) + 6x7f(x) (b) y = Oy' = O y' = xf(x) + 5f '(x) . O y'=xf '(x) - 5f(x) x6 Oy' = f(x) x5 xf '(x) - 4f(x) xf '(x) + 4f(x) x5 O y' = xf(x) - 5f '(x) = +4 y = - (c) x6 f(x) O y'= f'(x) (6x5) - x6f(x) [f(x)]² Oy' = f'(x) (5x5) - x6f '(x) [f(x)]² O y' = f(x)(5x6) + x6ƒ '(x) [f(x)]²

Q: Let f'(x) = f(x) = = 4x √8 - 6x

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Q: x 29. f(x) 1 + e*

A: Differentiating the given function by using quotient rule, we get

Q: What is the first derivative of the following function: f(x) = (x³ + 2)4 O f'(x) = 12x²(x³ + 2)³ O…

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Q: If f x = x3 - x ,find  f '''  and f 4 x

A: We first find the 1st and 2nd derivatives.

Q: Differentiate the function.

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Q: f(x) = 5x csc x 7 f (x) = 100 + 2cosx – 3x+x 3.

A: *formula:- d/dx (cscx) = -cscx*cotx. d/dx (x^{n}) = nx^{n-1}. d/dx (cosx) = -sinx.

Q: Find the derivative of f(x) = (x-2x)2 A) f'(x) = 6x5 - 12x3+ 8x B) f'(x) = 6x5- 16x3 + 8x %3D C)…

A: Here we find the derivatives of function.

Q: -4 Find f'(x) when f(x) = -

A: We will solve the problem

Q: Find the derivative of * T (x) = Va + 9 Væ? 2.

A: Given T(x)=x+9x73-2x25…

Q: In(3æ) Given f(x) the derivative f'(x) is 3 3 1 3x 1 3 1 3x

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Q: Find f. f ''(x) = 20x3 + 12x2 + 4,    f(0) = 6,    f(1) = 1 f(x) =

A: According to question,Given Derivative,f''x = 20x3 + 12x2 + 4,f0 =6,f1 = 1

Q: find f'(x) for f(x)= (5x-2)3 (1-x3)4

A: It is given that the function is

Q: Find f. f ''(x) = 4 + 6x + 24x2,    f(0) = 5,    f (1) = 14

A: To find out the function f whose double derivative and some initial conditions are given.

Q: Let f(x) = 2x² f'(x) = - T. The derivative function Select one: O x ² 2 O 3x² O 3x²2² O 3x² O None…

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Q: The derivative of the function f (x) = (x-1 – 2)(3 – Vx ) is, %3D 2x2 – x – 6/x A. fi(x) %3D 2x2+…

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Q: find f'(x) for f(x)= (2x-1)4 (3-x5)4

A: f(x)= (2x-1)4 (3-x5)4Let (2x - 1) = u and (3-x5) = vHence, du/dx = 2 and dv/dx = -5x4Also, f = u4v4…

Q: 2e* f (x) = x- 2e*

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Q: Find the f derivative of x given f(x)=(3x)^-1

A: Calculation:Compute the derivative of f(x) = (3x)−1 as follows.

Q: Find f '(a) for f(x) = 3 − 2x + 4x2

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Q: hen f has points of inflection when x =

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Q: Find f. f'(x)  = 5x4 - 3x2   + 4    , f(-1)  =2

A: we have to find the value of 'f' f'(x)  = 5x4  -3x2   + 4    , f(-1)  =2