(c) If f (2) = (2³ + 6) e'0-, 10z and f' (6i) = re®̟ then what is the value of r² ? < >

Q: 2x + 8 Find f'(x) if f(x) x² + 3 f'(x)

A:

Q: tx' 3 - - (³ 4) X X = C1 (1) +02 10 + ()

A:

Q: Find f. f"(x) = −4+ 8x - 12x², f(0) = 4, f'(0) = 12 (Prob. 1,

A: Consider the derivative function and initial conditions, f''x=-4+8x-12x2,f0=4,f'0=12 The objective…

Q: Find the function f(x) if f'(x) = ex+ 2 +(3/x) and f(1) = 6

A: We have to find the integral of f'(x) to obtain f(x) Steps: 1. Integrate with respect to x 2. Apply…

Q: Find f. f"(x)  =-2  +12 x -12 x2   , f(0)   = 4 ,f'(0)  =12

A: Given ,f''x=-2+12x-12x2f0=4f'0=12

Q: Find an expression for h'(x).  h(x) = 2 f (2x + 1)

A: Given equation - hx = 2f2x+1    .........(1)

Q: Differentiate. V(x) = (3x³ + 3)(x* – 2x) V '(x) =

A:

Q: If f'(x) = and f(0) = 2, then f(4)can be written in fully simpi %3D S(x)

A:

Q: 3x + 6 If f(x) find: 2x +2 f'(x) = f'(3) =

A:

Q: 6. 2х — 7 H(x) .2 х? + 3,

A: We will use Chain rule and Division rule of derivative

Q: h(x)=3(5x³ -2x² +6)'. Find h'(x).

A: Given, h(x) = 3(5x3 -2x2 +6 )7

Q: solve  w' + ((2w)/x) = x5,       w(0) = 1 what is w(1)

A:

Q: Given f"(x) = -7x³ – 7a? + 7x + 10, f'(1) = 7, and f(1) = 5. Find f'(x) and f(x). Part 1: Find the…

A:

Q: Find f. f ''(x) = x−2,    x > 0,    f(1) = 0,    f(7) = 0

A: I am going to solve the given problem by using some simple calculus to get the reqiuired result.

Q: +8x-x +2x +1 (x² + 3)(x' +1)

A: SImplification of the given function helps to find the required integrated function. The partial…

Q: y=x^2+2x+1 / x^2-2x+1 is equal to y'= -4(x+1) / (x-1)^3  True or False?

A: Simply and differentiate to get the answer.

Q: what's y'' of y=4secx csc x

A: Given; y=4secx csc x

Q: dz -i|=1 (22+i) "[( -- 1)]

A: We need to evaluate ∮z-i=1dzz2+i

Q: Let f(x) - 6e* +2 + e'. f'(0) =

A: The given function is f(x)=-6ex+2+e1

Q: 7x2 + 6x + 2 If f(x) then: f'(x) = f'(2) =

A: The given function is f(x)=7x2+6x+2x

Q: If 87 + 2 f(x) + 3x² (ƒ(x))³ = 0 and ƒ(1) = −3, find ƒ'(1).

A: 87+2f(x)+3x2(f(x))3=0,f(1)=−3

Q: Find a) (f(x^2). X=4 b) (g(f(x)). X= 3

A:

Q: If f(x) = 3/7(2 – 7a + 5), find f'(x). - Find f'(3).

A: Given:- f(x) = 3√x(x3-7√x+5)  To find:- f'(x) and f'(3)

Q: f"(x) = 2x – 4 and f'(-1) = -1 and f(-1) = -3. Find f'(x) = and find f(4) = %3D

A:

Q: Differentiate. G(x) = (8x² + 9) (4x + Vx) Gʻ(x) =D %3D

A: We know that, from product rule of differentiation ddxfx·gx=fx·g'x+gx·f'x                  ⋯⋯1 We…

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 d/dx f^-1 (4) where f(x)=4+2x^3+sin((pi*x)/2) for -1

A: We have,.We have to find .

Q: Find f. f ''(x) = −2 + 36x − 12x2,    f(0) = 5,    f '(0) = 18

A:

Q: Find f. f"(x) = -2 + 36x – 12x², (0) = 8, f'(0) = 18 "(x) =

A:

Q: If u(x) = x3, then du = 3x2.

A:

Q: If f'(x) = 9xe" and f(0) = -5, then f(x) =

A: